数理方程的虚边界元法及其与相关方法的关系

Virtual boundary element method for solving mathematical equations and relationship between it and relative methods

自1984年至今国内外在数理方程的数值解法中先后出现了叠加法、域外奇点法、虚边界元法和边界点（全特解场）法．这些方法之间虽然名称各异，但其理论基础是相同的．例如叠加法、域外奇点法、虚边界元一配点法和边界点法就是这样．阐明了虚边界元与其余方法的差异，并给出数值例题，表明了其优异的效果；另外证明上述四种方法理论基础是完全相同的，以便取得同行们的共识．

Since 1984, some numerical methods for solving mathematical equations, forexample, superposition method, out-domain singularity point method, virtualboundary-collocation method and boundary point (or whole special solution field) method, haveappeared early or late in the international and domestic journals. Although their names aredifferent but their theoretic foundation is all the same. This paper gives a proof theoretically onthis point on the one hand, and on the other hand, describes the differences among the virtualboundary element method and the rest methods mentioned above, and then gives out twoexamples to illustrate the effectiveness of VBELS (virtual boundary element-least Square)method.