We present a non-nested multilevel algorithm for solving the Poisson equation discretized at
scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We …

The use of multigrid and related preconditioners with the finite element method is often
limited by the difficulty of applying the algorithm effectively to a problem, especially when the …

In this paper, we developed and demonstrated a non-nested multilevel procedure for solving
the heat conduction equation in complex domains using a meshless discretization method …

This article presents an application of nonnested and unstructured multigrid methods to
linear elastic problems. A variational formulation for transfer operators and some multigrid …

A new interpolation/restriction operator based on a distance weight method proposed in the
Part I of this paper is adopted for multigrid method in the context of finite element method …

The construction of efficient interpolation/restriction operators is a key component for the
successful implementation of multigrid (MG) methods. Although numerous interpolation …

This thesis is concerned with the efficient numerical solution of nonlinear partial differential
equations (PDEs) of elliptic and parabolic type. Such PDEs arise frequently in models used …

Meshless methods using radial basis functions (RBF) are an attractive alternative to grid
based methods for solving partial differential equations in complex geometries. Gaussian …

In this work, multigrid procedures for the h and p versions of the FEM are discussed.
Multigrid methods have an optimal solution cost for linear elliptic problems. In this work, non …

This thesis encompasses a number of efforts towards the development of fast numerical
methods and their applications, particularly in light of the simulation of biochemical systems …