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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)

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)

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