numerical methods

The Lanczos algorithm

Finding the eigenvalues and eigenvectors of large hermitian matrices is a key problem of (numerical) quantum mechanics. Often, however, the matrices of interest are much too large to employ exact methods. A popular and powerful approximation method is based on the Lanczos algorithm. The Lanczos algorithm determines an orthonormal basis of the Kyrlov sub-space $\mathcal{K}_k(\Psi,… Continue reading The Lanczos algorithm


New TRNG release

A new version of TRNG (Tina’s Random Number Generator Library) has been released. TRNG may be utilized in sequential as well as in parallel Monte Carlo simulations. It does not depend on a specific parallelization technique, e.g., POSIX threads, MPI and others. The new version 4.17 is a bug fix and maintenance release.

GPU computing · MPI · parallel computing · Performance

CUDA-aware MPI

CUDA and MPI provide two different APIs for parallel programming that target very different parallel architectures. While CUDA allows to utilize parallel graphics hardware for general purpose computing, MPI is usually employed to write parallel programs that run on large SMP systems or on cluster computers. In order to improve a cluster’s overall computational capabilities… Continue reading CUDA-aware MPI

numerical methods · Python

Eigenvalues and eigenfunctions

Computing the eigenvectors $\psi(x)$ and eigenvalues $E$ of some Hamiltonian $H$ belongs to the key problems of quantum mechanics. For the one-dimensional Schrödinger equation we have to solve \begin{equation} E\psi(x) = H\psi(x) = -\frac{1}{2}\frac{\mathrm{d}^2\psi(x)}{\mathrm{d} x^2} + V(x)\psi(x) \end{equation}for some given potential $V(x)$. Analytical solutions, however, are scare goods. Thus, one has to rely on approximations… Continue reading Eigenvalues and eigenfunctions