Abstract
The numerical algorithm for fast computations with interface operators associated with the elliptic boundary value problems (BVP) defined on step-type domains is presented. The algorithm is based on the asymptotically almost optimal technique developed for treatment of the discrete Poincare-Steklov (PS) operators associated with the finite-difference Laplacian on rectangles when using the uniform grid with a `displacement by h/2`. The approach can be regarded as an extension of the method proposed for the partial solution of the finite-difference Laplace equation to the case of displaced grids and mixed boundary conditions. It is shown that the action of the PS operator for the Dirichlet problem and mixed BVP can be computed with expenses of the order of O(Nlog{sup 2}N) both for arithmetical operations and computer memory needs, where N is the number of unknowns on the rectangle boundary. The single domain algorithm is applied to solving the multidomain elliptic interface problems with piecewise constant coefficients. The numerical experiments presented confirm almost linear growth of the computational costs and memory needs with respect to the dimension of the discrete interface problem. 14 refs., 3 figs., 4 tabs.
Citation Formats
Khoromskij, B N, Mazurkevich, G E, and Nikonov, E G.
Cost-effective computations with boundary interface operators in elliptic problems.
JINR: N. p.,
1993.
Web.
Khoromskij, B N, Mazurkevich, G E, & Nikonov, E G.
Cost-effective computations with boundary interface operators in elliptic problems.
JINR.
Khoromskij, B N, Mazurkevich, G E, and Nikonov, E G.
1993.
"Cost-effective computations with boundary interface operators in elliptic problems."
JINR.
@misc{etde_10138856,
title = {Cost-effective computations with boundary interface operators in elliptic problems}
author = {Khoromskij, B N, Mazurkevich, G E, and Nikonov, E G}
abstractNote = {The numerical algorithm for fast computations with interface operators associated with the elliptic boundary value problems (BVP) defined on step-type domains is presented. The algorithm is based on the asymptotically almost optimal technique developed for treatment of the discrete Poincare-Steklov (PS) operators associated with the finite-difference Laplacian on rectangles when using the uniform grid with a `displacement by h/2`. The approach can be regarded as an extension of the method proposed for the partial solution of the finite-difference Laplace equation to the case of displaced grids and mixed boundary conditions. It is shown that the action of the PS operator for the Dirichlet problem and mixed BVP can be computed with expenses of the order of O(Nlog{sup 2}N) both for arithmetical operations and computer memory needs, where N is the number of unknowns on the rectangle boundary. The single domain algorithm is applied to solving the multidomain elliptic interface problems with piecewise constant coefficients. The numerical experiments presented confirm almost linear growth of the computational costs and memory needs with respect to the dimension of the discrete interface problem. 14 refs., 3 figs., 4 tabs.}
place = {JINR}
year = {1993}
month = {Dec}
}
title = {Cost-effective computations with boundary interface operators in elliptic problems}
author = {Khoromskij, B N, Mazurkevich, G E, and Nikonov, E G}
abstractNote = {The numerical algorithm for fast computations with interface operators associated with the elliptic boundary value problems (BVP) defined on step-type domains is presented. The algorithm is based on the asymptotically almost optimal technique developed for treatment of the discrete Poincare-Steklov (PS) operators associated with the finite-difference Laplacian on rectangles when using the uniform grid with a `displacement by h/2`. The approach can be regarded as an extension of the method proposed for the partial solution of the finite-difference Laplace equation to the case of displaced grids and mixed boundary conditions. It is shown that the action of the PS operator for the Dirichlet problem and mixed BVP can be computed with expenses of the order of O(Nlog{sup 2}N) both for arithmetical operations and computer memory needs, where N is the number of unknowns on the rectangle boundary. The single domain algorithm is applied to solving the multidomain elliptic interface problems with piecewise constant coefficients. The numerical experiments presented confirm almost linear growth of the computational costs and memory needs with respect to the dimension of the discrete interface problem. 14 refs., 3 figs., 4 tabs.}
place = {JINR}
year = {1993}
month = {Dec}
}