A kind of improved contact frictional model on basis of traditional Coulomb Friction model is adopted.Corresponding contact element is also given.The contact algorithm on basis of augmented Lagrange method is introduc...A kind of improved contact frictional model on basis of traditional Coulomb Friction model is adopted.Corresponding contact element is also given.The contact algorithm on basis of augmented Lagrange method is introduced and successfully applied to complex contact friction problem.Test example and actual engineering case all show that the algorithm of the model is efficient and computation results agree well with general rules.展开更多
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studi...Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.展开更多
In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by ad...In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.展开更多
In this paper,a passive muzzle arc control device(PMACD)of the augmented railguns is studied.By discussing its performance at different numbers of extra rails,a parameter optimization model is proposed.Through the cal...In this paper,a passive muzzle arc control device(PMACD)of the augmented railguns is studied.By discussing its performance at different numbers of extra rails,a parameter optimization model is proposed.Through the calculation model,it is found that the PMACD works well in the simple railgun,which refers to the gun that there is only one pair of rails in the inner bore.The PMACD may decrease the simple railgun’s armature peak current and muzzle arc,but affect its muzzle velocity not much.However,in the augmented railguns it has different characteristics.If the parameters of the PMACD are not selected suitable.It may increase the armature peak current and muzzle arc,but greatly decrease the velocity.The reason for this problem is that the extra rails generate a strong magnetic field in front of the armature,which induces a large current to change the armature current.It is also found that when the resistance and inductance parameters of the PMACD satisfy with the optimization formula,the PMACD can also play a good role in arc suppression in the augmented railguns.Experiments of an augmented railgun with a stainless steel PMACD are carried out to verify this optimization method.Results show that the muzzle arc is obviously controlled.This work may provide a reference for the design of the muzzle arc control device.展开更多
Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide ra...Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications in computer vision and pattern recognition. In this paper, we propose a new model to deal with the TRPCA problem by an alternation minimization algorithm along with two adaptive rankadjusting strategies. For the underlying low-rank tensor, we simultaneously perform low-rank matrix factorizations to its all-mode matricizations; while for the underlying sparse tensor,a soft-threshold shrinkage scheme is applied. Our method can be used to deal with the separation between either an exact or an approximate low-rank tensor and a sparse one. We established the subsequence convergence of our algorithm in the sense that any limit point of the iterates satisfies the KKT conditions. When the iteration stops, the output will be modified by applying a high-order SVD approach to achieve an exactly low-rank final result as the accurate rank has been calculated. The numerical experiments demonstrate that our method could achieve better results than the compared methods.展开更多
This paper proposes a semismooth Newton method for a class of bilinear programming problems(BLPs)based on the augmented Lagrangian,in which the BLPs are reformulated as a system of nonlinear equations with original va...This paper proposes a semismooth Newton method for a class of bilinear programming problems(BLPs)based on the augmented Lagrangian,in which the BLPs are reformulated as a system of nonlinear equations with original variables and Lagrange multipliers.Without strict complementarity,the convergence of the method is studied by means of theories of semismooth analysis under the linear independence constraint qualification and strong second order sufficient condition.At last,numerical results are reported to show the performance of the proposed method.展开更多
The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional ...The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.展开更多
The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the p...The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the popular optimal function coefficient(OFC),sphere cap harmonic analysis(SCHA),kriging and inverse distance weighting(IDW)interpolation in ZTD spatial prediction and Beidou satellite navigation system(BDS)-PPP augmentation over China.For ZTD spatial prediction,the average time consumption of the OFC,kriging,and IDW methods is less than 0.1 s,which is significantly better than that of the SCHA method(63.157 s).The overall ZTD precision of the OFC is 3.44 cm,which outperforms those of the SCHA(9.65 cm),Kriging(10.6 cm),and IDW(11.8 cm)methods.We confirmed that the low performance of kriging and IDW is caused by their weakness in modelling ZTD variation in the vertical direction.To mitigate such deficiencies,an elevation normalization factor(ENF)is introduced into the kriging and IDW models(kriging-ENF and IDW-ENF).The overall ZTD spatial prediction accuracies of IDW-ENF and kriging-ENF are 2.80 cm and 2.01 cm,respectively,which are both superior to those of the OFC and the widely used empirical model GPT3(4.92 cm).For BDS-PPP enhancement,the ZTD provided by the kriging-ENF,IDW-ENF and OFC as prior constraints can effectively reduce the convergence time.Compared with unconstrained BDS-PPP,our proposed kriging-ENF outperforms IDW-ENF and OFC by reducing the horizontal and vertical convergence times by approximately 13.2%and 5.8%in Ningxia and 30.4%and 7.84%in Guangdong,respectively.These results indicate that kriging-ENF is a promising method for ZTD spatial prediction and BDS-PPP enhancement over China.展开更多
Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and im...Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.展开更多
The immersed boundary method is well-known,popular,and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface.In this paper,an immersed b...The immersed boundary method is well-known,popular,and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface.In this paper,an immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains(exterior or interior)with a Dirichlet boundary condition.The new method inherits the simplicity,robustness,and first order convergence of the IB method but also provides asymptotic first order convergence of partial derivatives.Numerical examples are provided to confirm the analysis.展开更多
A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions...A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.展开更多
This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving t...This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm. Numerical results show that the approximate solutions to big-sized problems obtained by this method are superior to those by NFDH, FFDH and BFDH approaches.展开更多
Principal component analysis and generalized low rank approximation of matrices are two different dimensionality reduction methods. Two different dimensionality reduction algorithms are applied to the L1-CSVM model ba...Principal component analysis and generalized low rank approximation of matrices are two different dimensionality reduction methods. Two different dimensionality reduction algorithms are applied to the L1-CSVM model based on augmented Lagrange method to explore the variation of running time and accuracy of the model in dimensionality reduction space. The results show that the improved algorithm can greatly reduce the running time and improve the accuracy of the algorithm.展开更多
Power augmented ram （PAR）engine is a popular equipment to reduce the requirement of power for takeoff and improve aerodynamic performance. To provide detailed insight into the aerodynamic characteristics of wing-in-...Power augmented ram （PAR）engine is a popular equipment to reduce the requirement of power for takeoff and improve aerodynamic performance. To provide detailed insight into the aerodynamic characteristics of wing-in-ground effect （WIG）craft with PAR engine, numerical simulations are carried out on WIG craft models in cruise. Simplified engine models are applied to the simulations. Two cruise modes for PAR engine are considered. The aerodynamic characteristics of the WIG craft and other features are studied. Comparisons with WIG craft model without PAR show that shutoff of PAR engine results in an increase in drag and less change in lift. Accordingly for the work of PAR engine, the air flow blown from the engine accelerates the flow around the upper surface and a high-speed attached flow near the trailing edge is recorded. With the schemed PAR flow, more suction force is realized and the flow features over the wing vary noticeably. It is also shown that the Coanda effect,provided with an attached flow, introduces an appropriate and practical flow mode for WIG craft with PAR engine in cruise. The results refresh our understanding on aerodynamic characteristics of WIG craft.展开更多
In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the ...In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.展开更多
We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting ...We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstrate the efficiency and accuracy of the methods. In these examples we use the proposed augmentation method to solve large scale linear systems resulting from the recently developed wavelet Galerkin methods and fast collocation methods applied to integral equations of the secondkind. Our numerical results confirm that this augmentation method is particularly efficient for solving large scale linear systems induced from wavelet compression schemes.展开更多
Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem d...Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.展开更多
In this paper,an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product domains.Through a correction step,the augmented two-scale finite element...In this paper,an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product domains.Through a correction step,the augmented two-scale finite element solution is obtained by solving an eigenvalue problem on a low-dimensional augmented subspace.Theoretical analysis and numerical experiments show that the augmented two-scale finite element solution achieves the same order of accuracy as the standard finite element solution on a fine grid,but the computational cost required by the former solution is much lower than that demanded by the latter.The augmented two-scale finite element method also improves the approximation accuracy of eigenfunctions in the L^(2)(Ω)norm compared with the two-scale finite element method.展开更多
In this paper,we analyze the convergence properties of a stochastic augmented Lagrangian method for solving stochastic convex programming problems with inequality constraints.Approximation models for stochastic convex...In this paper,we analyze the convergence properties of a stochastic augmented Lagrangian method for solving stochastic convex programming problems with inequality constraints.Approximation models for stochastic convex programming problems are constructed from stochastic observations of real objective and constraint functions.Based on relations between solutions of the primal problem and solutions of the dual problem,it is proved that the convergence of the algorithm from the perspective of the dual problem.Without assumptions on how these random models are generated,when estimates are merely sufficiently accurate to the real objective and constraint functions with high enough,but fixed,probability,the method converges globally to the optimal solution almost surely.In addition,sufficiently accurate random models are given under different noise assumptions.We also report numerical results that show the good performance of the algorithm for different convex programming problems with several random models.展开更多
文摘A kind of improved contact frictional model on basis of traditional Coulomb Friction model is adopted.Corresponding contact element is also given.The contact algorithm on basis of augmented Lagrange method is introduced and successfully applied to complex contact friction problem.Test example and actual engineering case all show that the algorithm of the model is efficient and computation results agree well with general rules.
文摘Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.
基金Supported by National Natural Science Foundation of China (No.51275348)College Students Innovation and Entrepreneurship Training Program of Tianjin University (No.201210056339)
文摘In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.
基金acknowledge the Fundamental Research Funds for the Central Universities(Grants No 309190112102)the Natural Science Foundation of Jiangsu Province(Grants No BK20200493).
文摘In this paper,a passive muzzle arc control device(PMACD)of the augmented railguns is studied.By discussing its performance at different numbers of extra rails,a parameter optimization model is proposed.Through the calculation model,it is found that the PMACD works well in the simple railgun,which refers to the gun that there is only one pair of rails in the inner bore.The PMACD may decrease the simple railgun’s armature peak current and muzzle arc,but affect its muzzle velocity not much.However,in the augmented railguns it has different characteristics.If the parameters of the PMACD are not selected suitable.It may increase the armature peak current and muzzle arc,but greatly decrease the velocity.The reason for this problem is that the extra rails generate a strong magnetic field in front of the armature,which induces a large current to change the armature current.It is also found that when the resistance and inductance parameters of the PMACD satisfy with the optimization formula,the PMACD can also play a good role in arc suppression in the augmented railguns.Experiments of an augmented railgun with a stainless steel PMACD are carried out to verify this optimization method.Results show that the muzzle arc is obviously controlled.This work may provide a reference for the design of the muzzle arc control device.
基金Supported by the National Natural Science Foundation of China(Grant Nos.6157209961320106008+2 种基金91230103)National Science and Technology Major Project(Grant Nos.2013ZX040050212014ZX04001011)
文摘Tensor robust principal component analysis（TRPCA） problem aims to separate a low-rank tensor and a sparse tensor from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications in computer vision and pattern recognition. In this paper, we propose a new model to deal with the TRPCA problem by an alternation minimization algorithm along with two adaptive rankadjusting strategies. For the underlying low-rank tensor, we simultaneously perform low-rank matrix factorizations to its all-mode matricizations; while for the underlying sparse tensor,a soft-threshold shrinkage scheme is applied. Our method can be used to deal with the separation between either an exact or an approximate low-rank tensor and a sparse one. We established the subsequence convergence of our algorithm in the sense that any limit point of the iterates satisfies the KKT conditions. When the iteration stops, the output will be modified by applying a high-order SVD approach to achieve an exactly low-rank final result as the accurate rank has been calculated. The numerical experiments demonstrate that our method could achieve better results than the compared methods.
基金Supported by the National Natural Science Foundation of China(No.11671183)the Fundamental Research Funds for the Central Universities(No.2018IB016,2019IA004,No.2019IB010)
文摘This paper proposes a semismooth Newton method for a class of bilinear programming problems(BLPs)based on the augmented Lagrangian,in which the BLPs are reformulated as a system of nonlinear equations with original variables and Lagrange multipliers.Without strict complementarity,the convergence of the method is studied by means of theories of semismooth analysis under the linear independence constraint qualification and strong second order sufficient condition.At last,numerical results are reported to show the performance of the proposed method.
基金supported by the National Natural Science Foundation of China(No.10771031)the Fundamental Research Funds for Central Universities(No.090405013)
文摘The successive overrelaxation-like （SOR-like） method with the real param- eters ω is considered for solving the augmented system. The new method is called the modified SOR-like （MSOR-like） method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like （Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel ＆ Scientific Computations, 7（4）, 453-462 （1999）） and the modified sym- metric SOR-like （MSSOR-like） methods （Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228（4）, 424-433 （2009））.
基金co-supported by the National Nature Science Foundation of China(No.12303071)the Shanghai Science and Technology Plan Project,China(No.23YF1455500)+1 种基金the China Postdoctoral Science Foundation(No.2023M743653)Ministry of Industry and Information Technology of China through the High Precision Timing Service Project(No.TC220A04A-80)。
文摘The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the popular optimal function coefficient(OFC),sphere cap harmonic analysis(SCHA),kriging and inverse distance weighting(IDW)interpolation in ZTD spatial prediction and Beidou satellite navigation system(BDS)-PPP augmentation over China.For ZTD spatial prediction,the average time consumption of the OFC,kriging,and IDW methods is less than 0.1 s,which is significantly better than that of the SCHA method(63.157 s).The overall ZTD precision of the OFC is 3.44 cm,which outperforms those of the SCHA(9.65 cm),Kriging(10.6 cm),and IDW(11.8 cm)methods.We confirmed that the low performance of kriging and IDW is caused by their weakness in modelling ZTD variation in the vertical direction.To mitigate such deficiencies,an elevation normalization factor(ENF)is introduced into the kriging and IDW models(kriging-ENF and IDW-ENF).The overall ZTD spatial prediction accuracies of IDW-ENF and kriging-ENF are 2.80 cm and 2.01 cm,respectively,which are both superior to those of the OFC and the widely used empirical model GPT3(4.92 cm).For BDS-PPP enhancement,the ZTD provided by the kriging-ENF,IDW-ENF and OFC as prior constraints can effectively reduce the convergence time.Compared with unconstrained BDS-PPP,our proposed kriging-ENF outperforms IDW-ENF and OFC by reducing the horizontal and vertical convergence times by approximately 13.2%and 5.8%in Ningxia and 30.4%and 7.84%in Guangdong,respectively.These results indicate that kriging-ENF is a promising method for ZTD spatial prediction and BDS-PPP enhancement over China.
文摘Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.
文摘The immersed boundary method is well-known,popular,and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface.In this paper,an immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains(exterior or interior)with a Dirichlet boundary condition.The new method inherits the simplicity,robustness,and first order convergence of the IB method but also provides asymptotic first order convergence of partial derivatives.Numerical examples are provided to confirm the analysis.
文摘A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.
基金State Foundstion of Ph.D Units of China(2003-05)under Grant 20020141013the NNSF(10471015)of Liaoning Province,China.
文摘This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm. Numerical results show that the approximate solutions to big-sized problems obtained by this method are superior to those by NFDH, FFDH and BFDH approaches.
文摘Principal component analysis and generalized low rank approximation of matrices are two different dimensionality reduction methods. Two different dimensionality reduction algorithms are applied to the L1-CSVM model based on augmented Lagrange method to explore the variation of running time and accuracy of the model in dimensionality reduction space. The results show that the improved algorithm can greatly reduce the running time and improve the accuracy of the algorithm.
基金Program for Changjiang Scholars and Innovative Research Team in UniversityDoctoral Program Foundation of Institutions of Higher Education of China (20060247028)
文摘Power augmented ram （PAR）engine is a popular equipment to reduce the requirement of power for takeoff and improve aerodynamic performance. To provide detailed insight into the aerodynamic characteristics of wing-in-ground effect （WIG）craft with PAR engine, numerical simulations are carried out on WIG craft models in cruise. Simplified engine models are applied to the simulations. Two cruise modes for PAR engine are considered. The aerodynamic characteristics of the WIG craft and other features are studied. Comparisons with WIG craft model without PAR show that shutoff of PAR engine results in an increase in drag and less change in lift. Accordingly for the work of PAR engine, the air flow blown from the engine accelerates the flow around the upper surface and a high-speed attached flow near the trailing edge is recorded. With the schemed PAR flow, more suction force is realized and the flow features over the wing vary noticeably. It is also shown that the Coanda effect,provided with an attached flow, introduces an appropriate and practical flow mode for WIG craft with PAR engine in cruise. The results refresh our understanding on aerodynamic characteristics of WIG craft.
文摘In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.
基金Supported in part by the Natural Science Foundation of China under grants 10371137and 10201034Foundation of Doctoral Program of National Higher Education of China under under grant 20030558008Guangdong Provincial Natural Science Foundation of China u
文摘We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstrate the efficiency and accuracy of the methods. In these examples we use the proposed augmentation method to solve large scale linear systems resulting from the recently developed wavelet Galerkin methods and fast collocation methods applied to integral equations of the secondkind. Our numerical results confirm that this augmentation method is particularly efficient for solving large scale linear systems induced from wavelet compression schemes.
文摘Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.
基金supported by the National Key R&D Program of China under Grant Nos.2019YFA0709600 and 2019YFA0709601the National Natural Science Foundation of China under Grant No.12021001+2 种基金supported by the National Natural Science Foundation of China under Grant No.92270206supported by the National Natural Science Foundation of China(Grant No.11771467)the disciplinary funding of Central University of Finance and Economics.
文摘In this paper,an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product domains.Through a correction step,the augmented two-scale finite element solution is obtained by solving an eigenvalue problem on a low-dimensional augmented subspace.Theoretical analysis and numerical experiments show that the augmented two-scale finite element solution achieves the same order of accuracy as the standard finite element solution on a fine grid,but the computational cost required by the former solution is much lower than that demanded by the latter.The augmented two-scale finite element method also improves the approximation accuracy of eigenfunctions in the L^(2)(Ω)norm compared with the two-scale finite element method.
基金supported by the National Key R&D Program of China(Project No.2022YFA1004000)by the Natural Science Foundation of China(Project No.12371298).
文摘In this paper,we analyze the convergence properties of a stochastic augmented Lagrangian method for solving stochastic convex programming problems with inequality constraints.Approximation models for stochastic convex programming problems are constructed from stochastic observations of real objective and constraint functions.Based on relations between solutions of the primal problem and solutions of the dual problem,it is proved that the convergence of the algorithm from the perspective of the dual problem.Without assumptions on how these random models are generated,when estimates are merely sufficiently accurate to the real objective and constraint functions with high enough,but fixed,probability,the method converges globally to the optimal solution almost surely.In addition,sufficiently accurate random models are given under different noise assumptions.We also report numerical results that show the good performance of the algorithm for different convex programming problems with several random models.
