Christoph W. Ueberhuber

The Concept of B-Convergence

A useful concept of convergence for nonlinear stiff ODE’s will be developed, which permits the derivation of uniform global error bounds independent of the stiffness of the considered problem. This concept will be discussed for three simple methods for stiff systems, the implicit Euler scheme, the implicit midpoint rule and the implicit trapezoidal rule.

Numerical integration on advanced computer systems

Applications of numerical integration.- Fundamentals of numerical integration.- Integrals.- Univariate integration formulas.- Multivariate integration formulas.- Integration algorithms.- Load distribution.- Potential parallelism in integration algorithms.- Parallelization schemes for integration algorithms.- Practical parallelization of integration algorithms.- Parallel data management.- Assessment of numerical integration software.- Architecture adaptive integration algorithms.

Stability Properties of Implicit Runge–Kutta Methods

New stability concepts—

ITERATED DEFECT CORRECTION FOR THE EFFICIENT SOLUTION OF STIFF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

BS

Large-scale electronic structure calculations of high-Z metals on the BlueGene/L platform

-stability and

Efficient Utilization of SIMD Extensions

BSI

Large-Scale First-Principles Molecular Dynamics simulations on the BlueGene/L Platform using the Qbox code

-stability (internal

Iterated defect correction for differential equations part I: theoretical results

BS

Spectral decomposition of real circulant matrices

-stability)—are introduced.

Vectorization techniques for the Blue Gene/L double FPU

BS