Scalable domain decomposition preconditioner for Navier–Stokes equations coupled with the heat equation

A High-Order Domain Decomposition algorithm for the Heat Equation

To solve the heat equation on parallel computers, a high-order finite difference domain decomposition algorithm is discussed. In this procedure, interface values between subdomains are calculated by the classical explicit scheme, while interior values of sub-domains are determined by the famous forth-order compact scheme. The stability and convergence for this domain decomposition algorithm are...

Analysis of a Scalable Preconditioner for the Wigner-poisson Equation

We analyze a preconditioner for the time-independent Wigner-Poisson equations for a resonant tunneling diode and present a numerical example of a continuation study which supports the theory. The application of the preconditioner transforms the equations into a compact fixed point problem for the Wigner distribution. After discretization, the Jacobians of the discrete problem have mesh-independ...

An Interface Strip Preconditioner for Domain Decomposition Methods: Application to the Coupled Surface and Groundwater Flow

In this paper, the efficiency of a parallelizable preconditioner for Domain Decomposition Methods in the context of the solution of non-symmetric linear equations arising from the discretization of the conservation laws in hydrology (e.g., the coupled surface and sub-surface flow over a freatic acuifer) is investigated. The Interface Strip Preconditioner (IS) proposed is based on solving a prob...

A domain decomposition preconditioner of Neumann-Neumann type for the Stokes equations

Parallel Subdomain-based Preconditioner for Non-overlapping Domain Decomposition Methods Parallel Subdomain-based Preconditioner for Non-overlapping Domain Decomposition Methods

We present a new parallelizable preconditioner that is used as the local component for a two-level preconditioner similar to BPS. On 2D model problems that exhibit either high anisotropy or discontinuity, we demonstrate its attracting numerical behaviour and compare it to the regular BPS. Finally, to alleviate the construction cost of this new preconditioner, that requires the explicit computat...