Online citations, reference lists, and bibliographies.

A Kansa Type Method Using Fundamental Solutions Applied To Elliptic PDEs

C. Alves, S. Valtchev
Published 2007 · Mathematics

Cite This
Download PDF
Analyze on Scholarcy
A Kansa type modification of the Method of Fundamental Solutions (MFS) is presented. This allows us to apply the MFS to a larger class of elliptic problems. In the case of inhomogeneous problems we reduce to a single linear system, contrary to previous methods where two linear systems are solved, one for the particular solution and one for the homogeneous solution of the problem. Here the solution is approximated using fundamental solutions of the Helmholtz equation. Several numerical tests in 2D will be presented in order to illustrate the convergence of the method. Mixed, Dirichlet-Neumann, boundary conditions will be considered.
This paper references

This paper is referenced by
Hybrid meshless method for numerical solution of partial differential equations
Jeanette Marie Monroe (2014)
Efficient Kansa-type MFS algorithm for time-fractional inverse diffusion problems
Liang Yan (2014)
A Kansa-type MFS scheme for two-dimensional time fractional diffusion equations
Liang Yan (2013)
On the application of the method of fundamental solutions to nonlinear partial differential equations
Carlos J. S. Alves (2018)
Efficient Kansa-type MFS algorithm for elliptic problems
Andreas Karageorghis (2009)
Domain decomposition methods with fundamental solutions for Helmholtz problems with discontinuous source terms
Carlos J. S. Alves (2018)
Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear Poisson problems
Abdeljalil Tri (2014)
O Método das Soluções Fundamentais com Expansão em Multipolos
Moisés Viana Felipe de Oliveira (2016)
A time-marching MFS scheme for heat conduction problems
S. Valtchev (2008)
Maximal and minimal norm of Laplacian eigenfunctions in a given subdomain
Pedro R. S. Antunes (2016)
Efficient MFS Algorithms for Inhomogeneous Polyharmonic Problems
Andreas Karageorghis (2011)
High order continuation algorithm and meshless procedures to solve nonlinear Poisson problems
Abdeljalil Tri (2012)
Extending the method of fundamental solutions to non-homogeneous elastic wave problems
Carlos J. S. Alves (2017)
The method of approximate particular solutions for solving certain partial differential equations
C. Chen (2012)
A nonlinear eigenvalue optimization problem: Optimal potential functions
Pedro R. S. Antunes (2018)
A Meshfree Method with Fundamental Solutions for Inhomogeneous Elastic Wave Problems
Svilen S. Valtchev (2014)
On the choice of source points in the method of fundamental solutions
C. Alves (2009)
Semantic Scholar Logo Some data provided by SemanticScholar