Paul Ellinghaus

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The Wigner Monte Carlo method, based on the generation and annihilation of particles, has emerged as a promising approach to treat transient problems of quantum electron transport in nanostructures. Tackling these simulations in multiple spatial dimensions demands a parallelized approach to facilitate a practical application of the method in order to(More)
The Wigner formalism provides a convenient formulation of quantum mechanics in the phase space. Deterministic solutions of the Wigner equation are especially needed for problems where phase space quantities vary over several orders of magnitude and thus can not be resolved by the existing stochastic approaches. However, finite difference schemes have been(More)
The signed-particle Monte Carlo method for solving the Wigner equation has made multi-dimensional solutions numerically feasible. The latter is attributable to the concept of annihilation of independent indistinguishable particles, which counteracts the exponential growth in the number of particles due to generation. After the annihilation step, the(More)
—The Wigner equation can conveniently describe quantum transport problems in terms of particles evolving in the phase space. Improvements in the particle generation scheme of the Wigner Monte Carlo method are shown, which increase the accuracy of simulations as validated by comparison to exact solutions of the Schrödinger equation. Simulations with a(More)
Schur complement technique, an effective implementation of the weak Galerkin is developed a linear system involving unknowns only associated with element boundaries. In this talk, several numerical applications of weak Galerkin methods will be discussed. at extending the well-known DUNE framework for PDE simulations (see http://dune-project.org) to prepare(More)
We consider general block matrices, arising from a finite element (FE) discretization of a system of partial differential equations and the task to precondition those matrices, when solving large scale linear systems. The classical preconditioning methods for block matrices usually require a high quality approximation of a Schur complement matrix, which is(More)
A domain decomposition approach for the par-allelization of the Wigner Monte Carlo method allows the huge memory requirements to be distributed amongst many computational units, thereby making large multi-dimensional simulations feasible. Two domain decomposition techniques—a uniform slab and uniform block decom-position—are compared and the design and(More)
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