Fast iterative solvers for boundary value problems on a local spherical region
نویسندگان
چکیده
Boundary value problems on local spherical regions arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Meshless methods using radial basis functions (rbfs) provide a simple way to construct numerical solutions with high accuracy. However, the linear systems arising from these methods are usually ill-conditioned, which poses a challenge for iterative solvers. We construct preconditioners based on additive Schwarz methods to accelerate the solution process for solving boundary value problems on local spherical regions.
منابع مشابه
On Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کاملFast Multipole Accelerated Boundary Element Methods for the 3D Helmholtz Equation
Abstract The development of a fast multipole method accelerated iterative solution of the boundary element equations for large problems involving hundreds of thousands elements for the Helmholtz equations in 3D is described. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements) and the convergence criterion for iterative c...
متن کاملPreconditioning based on Calderon's formulae for periodic fast multipole methods for Helmholtz' equation
Solution of periodic boundary value problems is of interest in various branches of science and engineering such as optics, electromagnetics and mechanics. In our previous studies we have developed a periodic Fast Multipole Method (FMM) as a fast solver of wave problems in periodic domains. It has been found, however, that the convergence of the iterative solvers for linear equations slows down ...
متن کاملTitle Preconditioning based on Calderon’s formulae for periodic fast multipole methods for Helmholtz’ equation
Solution of periodic boundary value problems is of interest in various branches of science and engineering such as optics, electromagnetics and mechanics. In our previous studies we have developed a periodic Fast Multipole Method (FMM) as a fast solver of wave problems in periodic domains. It has been found, however, that the convergence of the iterative solvers for linear equations slows down ...
متن کاملNumerical Study on the Reaction Cum Diffusion Process in a Spherical Biocatalyst
In chemical engineering, several processes are represented by singular boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTM-Pad´e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for sol...
متن کامل