arXiv subjects

H. G. Kaper

Publications and source records attributed to H. G. Kaper.

4 recordsLinked to original sources

arXiv2001

A fast solver for systems of reaction-diffusion equations

In this paper we present a fast algorithm for the numerical solution of systems of reaction-diffusion equations, $\partial_t u + a \cdot \nabla u = Δu + F (x, t, u)$, $x \in Ω\subset \mathbf{R}^3$, $t > 0$. Here, $u$ is a vector-valued function, $u \equiv u(x, t) \in \mathbf{R}^m$, $m$ is large, and the corresponding system of ODEs, $\partial_t u = F(x, t, u)$, is stiff. Typical examples arise in air pollution studies, where $a$ is the given wind field and the nonlinear function $F$ models the atmospheric chemistry.

math.NA↗

arXiv2000

The frozen-field approximation and the Ginzburg-Landau equations of superconductivity

The Ginzburg--Landau (GL) equations of superconductivity provide a computational model for the study of magnetic flux vortices in type-II superconductors. In this article we show through numerical examples and rigorous mathematical analysis that the GL model reduces to the frozen-field model when the charge of the Cooper pairs (the superconducting charge carriers) goes to zero while the applied field stays near the upper critical field.

math.NA↗

arXiv2000

Implicit integration of the TDGL equations of superconductivity

This article is concerned with the integration of the time-dependent Ginzburg--Landau (TDGL) equations of superconductivity. Four algorithms, ranging from fully explicit to fully implicit, are presented and evaluated for stability, accuracy, and compute time. The benchmark problem for the evaluation is the equilibration of a vortex configuration in a superconductor that is embedded in a thin insulator and subject to an applied magnetic field.

math.NA↗

arXiv1999

Implicit Integration of the Time-Dependent Ginzburg-Landau Equations of Superconductivity

This article is concerned with the integration of the time-dependent Ginzburg-Landau (TDGL) equations of superconductivity. Four algorithms, ranging from fully explicit to fully implicit, are presented and evaluated for stability, accuracy, and compute time. The benchmark problem for the evaluation is the equilibration of a vortex configuration in a superconductor that is embedded in a thin insulator and subject to an applied magnetic field.

math.NA↗