This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit...This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.展开更多
A Hybrid Free-Form Deformation(HFFD)method is developed to improve shape preservation in mesh deformation for perforated surfaces,which traditional Free-Form Deformation(FFD)techniques struggle to handle effectively.T...A Hybrid Free-Form Deformation(HFFD)method is developed to improve shape preservation in mesh deformation for perforated surfaces,which traditional Free-Form Deformation(FFD)techniques struggle to handle effectively.The proposed method enables high-fidelity parameterized deformation for both flat and curved perforated surfaces while maintaining mesh quality with minimal geometric distortion.To evaluate its effectiveness,comparative studies between HFFD and conventional FFD methods are conducted,demonstrating superior performance in mesh quality and geometric fidelity.The HFFD-based framework is further applied to the Multidisciplinary Design Optimization(MDO)of a double-wall turbine blade leading edge.Results indicate an 11.6%increase in cooling efficiency and a 16.21%reduction in maximum stress.Additionally,compared to traditional geometry-based parameterization in MDO,the HFFD approach improves model processing efficiency by 84.15%and overall optimization efficiency by20.05%.These findings demonstrate HFFD's potential to significantly improve complex engineering design optimization by achieving precise shape preservation and improving computational efficiency.展开更多
Mesh models are among the primary representations for storing 3-D objects,encapsulating detailed geometric information.3-D mesh watermarking,in particular,plays a central role in the protection of 3-D content.However,...Mesh models are among the primary representations for storing 3-D objects,encapsulating detailed geometric information.3-D mesh watermarking,in particular,plays a central role in the protection of 3-D content.However,frequency-domain methods rely on complex parameterization and spectral decomposition,which are sensitive to mesh topology and resolution and often introduce perceptible artifacts.Spatial-domain techniques,on the other hand,typically embed watermarks in global or randomly selected regions,leading to visible distortions and reduced robustness.To address the above limitations and protect model copyright without compromising the original aesthetic quality,we propose a deterministice PCA-synchronized 3Dmeshwatermarkingmethodwith fullerene-guided carrier selection.First,a deterministic principal component analysis(PCA)-based mesh synchronization algorithm is employed to align the models to a canonical pose.Next,a fullerene-inspired carrier selection strategy is employed to determine the watermark carriers,leveraging the structural characteristics of fullerene molecules to achieve a more rational and effective carrier selection.Finally,to balance the embedding strength and enhance visual quality,the watermark information is embedded using an APQIM(Adaptive Parity-Check Quantization Index Modulation)scheme.The experimental results show that our method can achieve high visual quality with scalable capacity and strong robustness compared with existing methods.The watermarking scheme can resist various attacks,including simplification,smoothing,Gaussian noise,translation,and rotation.展开更多
Computing electrostatic interaction on non-cooperative targets with unknown meshes is crucial for electrostatic-based space on-orbit services.Although meshes for electrostatic interaction computations can be reconstru...Computing electrostatic interaction on non-cooperative targets with unknown meshes is crucial for electrostatic-based space on-orbit services.Although meshes for electrostatic interaction computations can be reconstructed from point clouds,they are usually too dense,leading to high computational costs.This paper presents an optimization method for converting dense meshes into optimal meshes,enabling fast and accurate computation of the electrostatic interaction by point clouds.First,the dense mesh reconstructed from point clouds is simplified into a coarse mesh using local operators.Second,the simplified mesh is refined by an iterative strategy that integrates a lightweight method of moments and an impedance matrix inheritance technique,ultimately yielding an optimal mesh for computing the electrostatic interaction.Simulation results show that our method effectively optimizes dense meshes,making electrostatic interaction computations using point clouds approximately 63.4 times more efficient than the previous method.展开更多
文摘This paper studies high order compact finite volume methods on non-uniform meshes for one-dimensional elliptic and parabolic differential equations with the Robin boundary conditions.An explicit scheme and an implicit scheme are obtained by discretizing the equivalent integral form of the equation.For the explicit scheme with nodal values,the algebraic system can be solved by the Thomas method.For the implicit scheme with both nodal values and their derivatives,the system can be implemented by a prediction-correction procedure,where in the correction stage,an implicit formula for recovering the nodal derivatives is introduced.Taking two point boundary value problem as an example,we prove that both the explicit and implicit schemes are convergent with fourth order accuracy with respect to some standard discrete norms using the energy method.Two numerical examples demonstrate the correctness and effectiveness of the schemes,as well as the indispensability of using non-uniform meshes.
基金supported by the National Science and Technology Major Project,China(No.2017-II-0006-0019)the National Natural Science Foundation of China(No.52375266)the Shaanxi Science Foundation for Distinguished Young Scholars,China(No.2022JC-36)。
文摘A Hybrid Free-Form Deformation(HFFD)method is developed to improve shape preservation in mesh deformation for perforated surfaces,which traditional Free-Form Deformation(FFD)techniques struggle to handle effectively.The proposed method enables high-fidelity parameterized deformation for both flat and curved perforated surfaces while maintaining mesh quality with minimal geometric distortion.To evaluate its effectiveness,comparative studies between HFFD and conventional FFD methods are conducted,demonstrating superior performance in mesh quality and geometric fidelity.The HFFD-based framework is further applied to the Multidisciplinary Design Optimization(MDO)of a double-wall turbine blade leading edge.Results indicate an 11.6%increase in cooling efficiency and a 16.21%reduction in maximum stress.Additionally,compared to traditional geometry-based parameterization in MDO,the HFFD approach improves model processing efficiency by 84.15%and overall optimization efficiency by20.05%.These findings demonstrate HFFD's potential to significantly improve complex engineering design optimization by achieving precise shape preservation and improving computational efficiency.
基金supported by the National Natural Science Foundation of China(NSFC)under Grant 62272331the Key Laboratory of Data Protection and Intelligent Management,Ministry of Education,Sichuan University and the Fundamental Research Funds for the Central Universities under Grant SCU2023D008.
文摘Mesh models are among the primary representations for storing 3-D objects,encapsulating detailed geometric information.3-D mesh watermarking,in particular,plays a central role in the protection of 3-D content.However,frequency-domain methods rely on complex parameterization and spectral decomposition,which are sensitive to mesh topology and resolution and often introduce perceptible artifacts.Spatial-domain techniques,on the other hand,typically embed watermarks in global or randomly selected regions,leading to visible distortions and reduced robustness.To address the above limitations and protect model copyright without compromising the original aesthetic quality,we propose a deterministice PCA-synchronized 3Dmeshwatermarkingmethodwith fullerene-guided carrier selection.First,a deterministic principal component analysis(PCA)-based mesh synchronization algorithm is employed to align the models to a canonical pose.Next,a fullerene-inspired carrier selection strategy is employed to determine the watermark carriers,leveraging the structural characteristics of fullerene molecules to achieve a more rational and effective carrier selection.Finally,to balance the embedding strength and enhance visual quality,the watermark information is embedded using an APQIM(Adaptive Parity-Check Quantization Index Modulation)scheme.The experimental results show that our method can achieve high visual quality with scalable capacity and strong robustness compared with existing methods.The watermarking scheme can resist various attacks,including simplification,smoothing,Gaussian noise,translation,and rotation.
基金supported by the National Natural Science Foundation of China(No.62003269).
文摘Computing electrostatic interaction on non-cooperative targets with unknown meshes is crucial for electrostatic-based space on-orbit services.Although meshes for electrostatic interaction computations can be reconstructed from point clouds,they are usually too dense,leading to high computational costs.This paper presents an optimization method for converting dense meshes into optimal meshes,enabling fast and accurate computation of the electrostatic interaction by point clouds.First,the dense mesh reconstructed from point clouds is simplified into a coarse mesh using local operators.Second,the simplified mesh is refined by an iterative strategy that integrates a lightweight method of moments and an impedance matrix inheritance technique,ultimately yielding an optimal mesh for computing the electrostatic interaction.Simulation results show that our method effectively optimizes dense meshes,making electrostatic interaction computations using point clouds approximately 63.4 times more efficient than the previous method.
