In this paper, we propose a method belonging to the class of special meshless kernel techniques for solving Poisson problems. The method is based on a simple new construction of an approximate particular solution of the nonhomogeneous equation in the space of polyharmonic splines. High order Lagrangian polyharmonic splines are used as a basis to approximate the nonhomogeneous term and a closed-form particular solution is given. The coefficients can be computed by convolution products of known vectors. This can be done in all dimensions, without numerical integration nor solution of systems. Numerical experiments are presented in two dimensions and show the quality of the approximations for different test examples
Bacchelli, B., Bozzini, M. (2009). Particular solution of poisson problems using Cardinal Lagrangian polyharmonic splines. In A. Ferreira, E.J. Kansa, G.E. Fasshauer, V. Leitão (a cura di), Progress on Meshless Methods (pp. 1-16). Barcellona : Springer [10.1007/978-1-4020-8821-6_1].
Particular solution of poisson problems using Cardinal Lagrangian polyharmonic splines
BACCHELLI, BARBARA;BOZZINI, MARIA TUGOMIRA
2009
Abstract
In this paper, we propose a method belonging to the class of special meshless kernel techniques for solving Poisson problems. The method is based on a simple new construction of an approximate particular solution of the nonhomogeneous equation in the space of polyharmonic splines. High order Lagrangian polyharmonic splines are used as a basis to approximate the nonhomogeneous term and a closed-form particular solution is given. The coefficients can be computed by convolution products of known vectors. This can be done in all dimensions, without numerical integration nor solution of systems. Numerical experiments are presented in two dimensions and show the quality of the approximations for different test examples
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