DeepAI
Log In Sign Up

Computational issues by interpolating with inverse multiquadrics: a solution

05/09/2022
by   Stefano De Marchi, et al.
0

We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly related to the computational cost of the multiplication between the coefficient matrix and the vectors computed by the solver at each iteration. We propose an efficient technique for the calculation of the product of the coefficient matrix and a generic vector. This computation is mainly based on the well-known spectral decomposition in spherical coordinates of the Green's function of the Laplacian operator. We also show the efficiency of the proposed method through numerical simulations.

READ FULL TEXT
04/29/2020

Preconditioned Legendre spectral Galerkin methods for the non-separable elliptic equation

The Legendre spectral Galerkin method of self-adjoint second order ellip...
04/09/2018

Computational identification of the lowest space-wise dependent coefficient of a parabolic equation

In the present work, we consider a nonlinear inverse problem of identify...
08/11/2020

An inverse spectral problem for a damped wave operator

This paper proposes a new and efficient numerical algorithm for recoveri...
10/19/2022

A fully implicit method using nodal radial basis functions to solve the linear advection equation

Radial basis functions are typically used when discretization sche-mes r...
05/25/2021

An efficient iterative method for solving parameter-dependent and random diffusion problems

This paper develops and analyzes a general iterative framework for solvi...
10/19/2022

Spectral methods for solving elliptic PDEs on unknown manifolds

In this paper, we propose a mesh-free numerical method for solving ellip...
10/04/2021

Optimal hybrid parameter selection for stable sequential solution of inverse heat conduction problem

To deal with the ill-posed nature of the inverse heat conduction problem...