Search
Now showing items 1-10 of 38
Optimal superconvergent one step nodal cubic spline collocation methods
(2006)
We formulate new optimal (fourth) order one step nodal cubic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the respective ...
Matrix decomposition algorithms for modified spline collocation for Helmholtz problems
(2003)
We consider the solution of various boundary value problems for the Helmholtz equation in the unit square using a nodal cubic spline collocation method and modifications of it which produce optimal (fourth-) order ...
The method of fundamental solutions for heat conduction in layered materials
(1999)
In this paper, we investigate the application of the Method of Fundamental Solutions (MFS) to two-dimensional problems of steady-state heat conduction in isotropic and anisotropic bimaterials. Two approaches are used: a ...
An hp finite element method for a 4th order singularly perturbed boundary value problem in two dimensions
(2017)
We consider a fourth order singularly perturbed boundary value problem posed in a square and the approximation of its solution by the hp version of the finite element method on the so-called Spectral Boundary Layer mesh. ...
An analytical method for linear elliptic PDEs and its numerical implementation
(2004)
A new numerical method for solving linear elliptic boundary value problems with constant coefficients in a polygonal domain is introduced. This method produces a generalized Dirichlet-Neumann map: given the derivative of ...
Comparison of two methods for the computation of singular solutions in elliptic problems
(1997)
We compare two numerical methods for the solution of elliptic problems with boundary singularities. The first is the integrated singular basis function method (ISBFM), a finite-element method in which the solution is ...
Conformal mapping for the efficient MFS solution of Dirichlet boundary value problems
(2008)
In this work, we use conformal mapping to transform harmonic Dirichlet problems of Laplace's equation which are defined in simply-connected domains into harmonic Dirichlet problems that are defined in the unit disk. We ...
Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains
(2007)
In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three-dimensional boundary value problems governed by elliptic systems of partial differential ...
Matrix decomposition MFS algorithms
(2006)
We describe the application of the Method of Fundamental Solutions (MFS) to elliptic boundary value problems in rotationally symmetric problems. In particular, we show how efficient matrix decomposition MFS algorithms can ...
A numerical conformal mapping method for harmonic mixed boundary value problems
(1996)
We describe a simple and versatile technique for the numerical solution of harmonic mixed boundary value problems in simply-connected domains. This technique is based on the theory of Riemann-Hilbert problems, and involves ...