Browsing by Subject "Fast Fourier transforms"
Now showing items 120 of 22

Article
Compact optimal quadratic spline collocation methods for the Helmholtz equation
(2011)Quadratic spline collocation methods are formulated for the numerical solution of the Helmholtz equation in the unit square subject to nonhomogeneous Dirichlet, Neumann and mixed boundary conditions, and also periodic ...

Article
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 simplyconnected domains into harmonic Dirichlet problems that are defined in the unit disk. We ...

Article
Conformal Mapping for the Efficient Solution of Poisson Problems with the KansaRBF Method
(2017)We consider the solution of Poisson Dirichlet problems in simplyconnected irregular domains. These domains are conformally mapped onto the unit disk and the resulting Poisson Dirichlet problems are solved efficiently using ...

Article
Efficient implementation of the MFS: The three scenarios
(2009)In this study we investigate the approximation of the solutions of harmonic problems subject to Dirichlet boundary conditions by the Method of Fundamental Solutions (MFS). In particular, we study the application of the MFS ...

Article
Efficient Kansatype MFS algorithm for elliptic problems
(2010)In this study we propose an efficient Kansatype method of fundamental solutions (MFSK) for the numerical solution of certain problems in circular geometries. In particular, we consider problems governed by the inhomogeneous ...

Article
Efficient MFS algorithms for inhomogeneous polyharmonic problems
(2011)In this work we develop an efficient algorithm for the application of the method of fundamental solutions to inhomogeneous polyharmonic problems, that is problems governed by equations of the form Δ ℓ u=f, ℓ ε ℕ, in circular ...

Article
Efficient MFS algorithms for problems in thermoelasticity
(2013)We propose efficient fast Fourier transform (FFT)based algorithms using the method of fundamental solutions (MFS) for the numerical solution of certain problems in planar thermoelasticity. In particular, we consider ...

Article
Efficient Trefftz collocation algorithms for elliptic problems in circular domains
(2013)We consider the numerical solution of certain elliptic boundary value problems in disks and annuli using the Trefftz collocation method. In particular we examine boundary value problems for the Laplace, Helmholtz, modified ...

Article
Finite Difference Schemes for the Cauchy–Navier Equations of Elasticity with Variable Coefficients
(2015)We solve the variable coefficient Cauchy–Navier equations of elasticity in the unit square, for Dirichlet and DirichletNeumann boundary conditions, using second order finite difference schemes. The resulting linear systems ...

Article
A KansaRadial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains
(2015)We employ a Kansaradial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains. This discretization leads, with an appropriate selection of collocation points and for ...

Article
KansaRBF algorithms for elliptic problems in axisymmetric domains
(2016)We employ a Kansaradial basis function method for the numerical solution of elliptic boundary value problems in threedimensional axisymmetric domains. We consider problems governed by the Poisson equation, the inhomogeneous ...

Conference Object
A KansaRBF method for Poisson problems in annular domains
(WITPress, 2014)We employ a Kansaradial basis function (RBF) method for Poisson boundary value problems in annular domains. This discretization leads, for any choice of RBF, to linear system matrices possessing block circulant structures. ...

Article
Matrix decomposition algorithms for elliptic boundary value problems: A survey
(2011)We provide an overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable ...

Article
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 ...

Article
A matrix decomposition MFS algorithm for biharmonic problems in annular domains
(2004)The Method of Fundamental Solutions (MFS) is a boundarytype method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution ...

Article
A matrix decomposition MFS algorithm for problems in hollow axisymmetric domains
(2006)In this work we apply the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation to certain axisymmetric harmonic and biharmonic problems. By exploiting the block circulant structure of the ...

Article
Matrix decomposition RBF algorithm for solving 3D elliptic problems
(2009)In this study, we propose an efficient algorithm for the evaluation of the particular solutions of threedimensional inhomogeneous elliptic partial differential equations using radial basis functions. The collocation points ...

Article
The method of fundamental solutions for elliptic problems in circular domains with mixed boundary conditions
(2015)We apply the method of fundamental solutions (MFS) for the solution of harmonic and biharmonic problems in circular domains subject to mixed boundary conditions. In contrast to the cases when boundary conditions of the ...

Article
The method of fundamental solutions for stationary heat conduction problems in rotationally symmetric domains
(2006)We propose an efficient boundary collocation method for the solution of certain two and threedimensional problems of steadystate heat conduction in Isotropie bimaterials. In particular, in two dimensions we consider the ...

Article
Modified nodal cubic spline collocation for threedimensional variable coefficient second order partial differential equations
(2013)We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate ...