研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导...研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。展开更多
This study presents a new boundary element method(BEM)framework for the numerical solution of general time-dependent or transient problems.By reformulating the time derivative as a domain integral,the framework effect...This study presents a new boundary element method(BEM)framework for the numerical solution of general time-dependent or transient problems.By reformulating the time derivative as a domain integral,the framework effectively decouples the treatment of spatial and temporal variables,allowing for the independent application of specialized discretization methods.For the temporal domain,we introduce an innovative time-spectral integration technique,which is based on Gaussian-quadrature-based orthogonal polynomial expansions.This method not only achieves arbitrary orders of accuracy but also significantly enhances computational efficiency and stability,particularly for simulations involving rapid transients or long-time dynamic simulations.The domain integrals in the spatial domain are calculated using the scaled coordinate transformation BEM(SCT-BEM),a mathematically rigorous technique that converts domain integrals into equivalent boundary integrals,preserving the boundary-only discretization advantage inherent in BEM.Numerical experiments on transient heat conduction and dynamic wave propagation further demonstrate the framework’s performance and capabilities.These experiments show that the proposed framework outperforms traditional time-stepping BEM methods,particularly in terms of stability,convergence rates,and computational cost,making it a highly promising tool for practical engineering applications.展开更多
文摘研究了复杂微细导线电容矩阵提取边界元法(boundary element method,BEM)的边界离散问题以及增强计算精度和数值稳定性的有效措施,分析了开阔边界尺寸、开阔边界离散、导线离散对计算精度的影响以及伪解、矩阵奇异性问题,提出了基于导线离散迭代和开阔边界迭代两阶段自动迭代边界元算法(automatic iterative boundary element method,AIBEM),并结合实例阐述了全域法和区域分解法两种多层介质问题系数矩阵生成方法。研究结果表明,边界环内生成的系数矩阵存在误差均衡协调问题,对复杂模型需合理选择各线段离散单元数及开阔边界尺寸,通过AIBEM可以获得经济的离散参数,有效避免矩阵奇异性,并提高收敛稳定性。将计算结果与有限元法、解析法、传输线法、矩量法进行了对比分析,证实了算法的可靠性。
基金supported by the National Natural Science Foundation of China(Grant Nos.12372199,12422207,and W2431010)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2021JQ02)the Ningbo Municipal Excellence Research Program(Zhejiang Province,China).
文摘This study presents a new boundary element method(BEM)framework for the numerical solution of general time-dependent or transient problems.By reformulating the time derivative as a domain integral,the framework effectively decouples the treatment of spatial and temporal variables,allowing for the independent application of specialized discretization methods.For the temporal domain,we introduce an innovative time-spectral integration technique,which is based on Gaussian-quadrature-based orthogonal polynomial expansions.This method not only achieves arbitrary orders of accuracy but also significantly enhances computational efficiency and stability,particularly for simulations involving rapid transients or long-time dynamic simulations.The domain integrals in the spatial domain are calculated using the scaled coordinate transformation BEM(SCT-BEM),a mathematically rigorous technique that converts domain integrals into equivalent boundary integrals,preserving the boundary-only discretization advantage inherent in BEM.Numerical experiments on transient heat conduction and dynamic wave propagation further demonstrate the framework’s performance and capabilities.These experiments show that the proposed framework outperforms traditional time-stepping BEM methods,particularly in terms of stability,convergence rates,and computational cost,making it a highly promising tool for practical engineering applications.
