The finite element method is a key player in computational electromag-netics for designing RF(Radio Frequency)components such as waveguides.The frequency-domain analysis is fundamental to identify the characteristics ...The finite element method is a key player in computational electromag-netics for designing RF(Radio Frequency)components such as waveguides.The frequency-domain analysis is fundamental to identify the characteristics of the components.For the conventional frequency-domain electromagnetic analysis using FEM(Finite Element Method),the system matrix is complex-numbered as well as indefinite.The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps.However,such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver.It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency.Overall,it is hard to adopt conventional iterative solvers even though the system matrix is sparse.A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper.In this implementation,the previous solution of the iterative solver of Matlab(Matrix Laboratory)employ-ing the preconditioner is used for the initial guess for the next step’s solution process.The overlapped parallel stage using Matlab’s Parallel Computing Toolbox is also proposed to alleviate the cold starting,which ruins the convergence of early steps in each parallel stage.Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.展开更多
The scattering of the open cavity filled with the inhomogeneous media is studied.The problem is discretized with a fourth order finite difference scheme and the immersed interfacemethod,resulting in a linear system of...The scattering of the open cavity filled with the inhomogeneous media is studied.The problem is discretized with a fourth order finite difference scheme and the immersed interfacemethod,resulting in a linear system of equations with the high order accurate solutions in the whole computational domain.To solve the system of equations,we design an efficient iterative solver,which is based on the fast Fourier transformation,and provides an ideal preconditioner for Krylov subspace method.Numerical experiments demonstrate the capability of the proposed fast high order iterative solver.展开更多
In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schu...In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.展开更多
The aim of this paper is to solve the two-dimensional acoustic scattering problems by random sphere using Electric field integral equation. Some approximations for the two-dimensional case are derived. These various a...The aim of this paper is to solve the two-dimensional acoustic scattering problems by random sphere using Electric field integral equation. Some approximations for the two-dimensional case are derived. These various approximations are next numerically validated in the case of high-frequency.展开更多
基金supported by Institute of Information&communications Technology Planning&Evaluation(ITP)grant funded by the Korea govermment(MSIT)(No.2019-0-00098,Advanced and Integrated Software Development for Electromagnetic Analysis)supported by Research Assistance Program(2021)in the Incheon National University.
文摘The finite element method is a key player in computational electromag-netics for designing RF(Radio Frequency)components such as waveguides.The frequency-domain analysis is fundamental to identify the characteristics of the components.For the conventional frequency-domain electromagnetic analysis using FEM(Finite Element Method),the system matrix is complex-numbered as well as indefinite.The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps.However,such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver.It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency.Overall,it is hard to adopt conventional iterative solvers even though the system matrix is sparse.A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper.In this implementation,the previous solution of the iterative solver of Matlab(Matrix Laboratory)employ-ing the preconditioner is used for the initial guess for the next step’s solution process.The overlapped parallel stage using Matlab’s Parallel Computing Toolbox is also proposed to alleviate the cold starting,which ruins the convergence of early steps in each parallel stage.Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.
基金The author is grateful for Professor Tao Tang and Dr.Zhonghua Qiao for many helpful and fruitful discussions,and would like to thank Professor Weiwei Sun for constructive suggestions。
文摘The scattering of the open cavity filled with the inhomogeneous media is studied.The problem is discretized with a fourth order finite difference scheme and the immersed interfacemethod,resulting in a linear system of equations with the high order accurate solutions in the whole computational domain.To solve the system of equations,we design an efficient iterative solver,which is based on the fast Fourier transformation,and provides an ideal preconditioner for Krylov subspace method.Numerical experiments demonstrate the capability of the proposed fast high order iterative solver.
基金developed in the framework of the associated team PhyLeas(Study of parallel hybrid sparse linear solvers) funded by INRIA where the partners are INRIA,T.U.Brunswick and University of Minnesotasupported by the US Department of Energy under grant DE-FG-08ER25841 and by the Minnesota Supercomputer Institute.
文摘In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.
文摘The aim of this paper is to solve the two-dimensional acoustic scattering problems by random sphere using Electric field integral equation. Some approximations for the two-dimensional case are derived. These various approximations are next numerically validated in the case of high-frequency.
