The pure boundary element method (BEM) is effective for the solution of a large class of problems. The main appeal of this BEM (reduction of the problem dimension by one) is tarnished to some extent when a fundamental solution to the governing equations does not exist as in the case of nonlinear problems. The easy to implement local point interpolation method applied to the strong form of differential equations is an attractive numerical approach. Its accuracy deteriorates in the presence of Neumann-type boundary conditions which are practically inevitable in solid mechanics. The main appeal of the BEM can be maintained by a judicious coupling of the pure BEM with the local point interpolation method. The resulting approach, named the LPI-BEM, seems versatile and effective. This is demonstrated by considering some linear and nonlinear elasticity problems including multi-physics and multi-field problems.

中文翻译：

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耦合边界元法和局部点插值求解各向异性弹性非线性、多物理场和多场问题

纯边界元法（BEM）对于解决一大类问题是有效的。当控制方程的基本解不存在时，这种边界元法（将问题维数减少一）的主要吸引力（如非线性问题的情况）在一定程度上受到损害。应用于强形式微分方程的易于实现的局部点插值方法是一种有吸引力的数值方法。在存在固体力学中几乎不可避免的诺伊曼型边界条件的情况下，其精度会降低。BEM 的主要吸引力可以通过纯 BEM 与局部点插值方法的明智耦合来保持。由此产生的方法，命名为 LPI-BEM，似乎通用且有效。