DeepAI AI Chat
Log In Sign Up

Selection of Sparse Sets of Influence for Meshless Finite Difference Methods

by   Oleg Davydov, et al.
Universität Gießen

We suggest an efficient algorithm for the selection of sparse subsets of a set of influence for the numerical discretization of differential operators on irregular nodes with polynomial consistency of a given order with the help of the QR decomposition of an appropriately weighted polynomial collocation matrix, and prove that the accuracy of the resulting numerical differentiation formulas is comparable with that of the formulas generated on the original set of influence.


page 1

page 2

page 3

page 4


Improved Stencil Selection for Meshless Finite Difference Methods in 3D

We introduce a geometric stencil selection algorithm for Laplacian in 3D...

Approximation with Conditionally Positive Definite Kernels on Deficient Sets

Interpolation and approximation of functionals with conditionally positi...

Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systems

For a wide class of polynomially nonlinear systems of partial differenti...

Chordal Graphs in Triangular Decomposition in Top-Down Style

In this paper, we first prove that when the associated graph of a polyno...

Sparse trace tests

We establish how the coefficients of a sparse polynomial system influenc...

New bounds and efficient algorithm for sparse difference resultant

Let P={P_0,P_1,...,P_n} be a generic Laurent transformally essential sys...

Costate Convergence with Legendre-Lobatto Collocation for Trajectory Optimization

This paper introduces a new method of discretization that collocates bot...