报告题目：The Method of Fundamental Solutions: Theory and Applications

报告人：黄宏财 教授

报告人单位：台湾义守大学

报告时间：2024年11月27日上午10:00-11:00

会议地点：#腾讯会议：839-338-407

主办单位：曲阜师范大学数学科学学院

报告摘要：The fundamental solutions (FS) satisfy the governing equations in a solution domain S, and then the numerical solutions can be found from the exterior and the interior boundary conditions on ∂S. The resource nodes of FS are chosen outside S, distinctly from the case of the boundary element method (BEM). This method is called the method of fundamental solutions (MFS), which originated from Kupradze in 1963. The Laplace and the Helmholtz equations are studied in detail, and biharmonic equations and the Cauchy-Navier equation of linear elastostatics are also discussed. Moreover, better choices of source nodes are explored. The simplicity of numerical algorithms and high accuracy of numerical solutions are two remarkable advantages of the MFS. However, the ill-conditioning of the MFS is notorious, and the condition number (Cond) grows exponentially via the number of the unknowns used. In this book, the numerical algorithms are introduced and their characteristics are addressed. The main efforts are made to establish the theoretical analysis in errors and stability. The strict analysis (as well as choices of source nodes) in this book has provided the solid theoretical basis of the MFS, to grant it to become an effective and competent numerical method for partial differential equations (PDE). Based on some of our works published as journal papers, this book presents essential and important elements of the MFS. It is intended for researchers, graduated students, university students, computational experts, mathematicians and engineers. In this talk, we only focus on the new locations of source nodes for MFS solving Laplace’s equation: pseudo radial-lines.

报告人简介：

黄宏财，台湾义守大学资料科学与大数据分析学系教授。2003年博士毕业于台湾中山大学，师从李子才教授，研究方向为数值分析和科学计算。在Engineering Analysis with Boundary Elements, Applied Numerical Mathematics, J. Computational and Applied Mathematics, Numerical Linear Algebra with Applications等国际重要期刊发表论文四十余篇，合作完成三本专著。多次参加国际会议并给出会议报告或者海报。