Rainer Roitzsch

A self‐adaptive multilevel finite element method for the stationary Schrödinger equation in three space dimensions

An error controlled finite element method (FEM) for solving stationary Schrodinger equations in three space dimensions is proposed. The method is based on an adaptive space discretization into tetrahedra and local polynomial basis functions of order p=1–5 defined on these tetrahedra. According to a local error estimator, the triangulation is automatically adapted to the solution. Numerical results for standard problems appearing in vibrational motion and molecular structure calculations are presented and discussed. Relative precisions better than 1e‐8 are obtained. For equilateral H++3, the adaptive FEM turns out to be superior to global basis set expansions in the literature. Our precise FEM results exclude in a definite manner the stability or metastability of equilateral H++3 in its ground state.

An object-oriented adaptive finite element code: design issues and applications in hyperthermia threatment planning

The finite element code Kaskade has been developed for the solution of partial differential equations in one, two, and three space dimensions. Its object-oriented implementation concept is based on the programming language C++. Adaptive finite element techniques are employed to provide solution procedures of optimal computational complexity. This implies a posteriori error estimation, local mesh refinement and multilevel preconditioning.

Simulation of the Transient Heating in an Unsymmetrical Coated Hot-Strip Sensor with a Self-Adaptive Finite Element Method

The transient heating in an unsymmetrical, coated, hot-strip sensor was simulated with a self-adaptive finite-element method (SAFEM). The first tests of this model show that it can be used to determine, with a small error, the thermal conductivity of liquids, from the transient temperature rise in the hot strip, which is deposited in a substrate and coated by an alumina spray.

KASKADE 3.x ein objektorientierter adaptiver Finite-Elemente-Code

KASKADE 3.x ist ein umfangreiches Programmpaket zur numerischen Losung von partiellen Differentialgleichungen mit adaptiven Finite-Elemente-Methoden. Der Gewinn der verwendeten Multilevel-Techniken besteht in der Verbindung von Zuverlassigkeit und Effizienz. Deshalb bietet das Programm — neben den Routinen zur Durchf uhrung adaptiver Gitterverfeinerung — ein groses Angebot an L osern f ur die auftretenden linearen Gleichungssysteme. Lineare L oser und Vorkonditionierer k onnen flexibel kombiniert werden.