RBF approximation of three dimensional PDEs using tensor Krylov subspace methods

In this paper, we propose different algorithms for the solution of a tensor linear discrete ill-posed problem arising in application meshless method solving PDEs three-dimensional space using multiquadric radial basis functions. It is well known that truncated singular value decomposition (TSVD) most common effective solver ill-conditioned systems, but unfortunately operation count system with TSVD computationally expensive large-scale matrices. present work, based on use Einstein product two tensors to define global Arnoldi and Gloub Kahan bidiagonalization algorithms. Using so-called Tikhonov regularization technique, will be able provide computable approximate regularized solutions few iterations. The formulation allow us develop an RBF approximation high dimensional Hierarchical Adaptive Cross Approximation, which turn reduces significantly storage computational costs, while accuracy preserved. performance proposed methods illustrated variety benchmark examples industrial applications degrees freedom.