ADER-WENO Finite volume schemes with adaptive mesh refinement for hyperbolic problems

In this work it is presented an ADER-WENO approach for hyperbolic problems in the context of the finite volume method, using adaptive mesh refinement. ADER approach is of great interest for time integration since it achieves an arbitrary order of accuracyin a single time step. This is a joint work with M. Dumbser and O. Zanotti from the University of Trento (Italy)

Critical points of the optimal quantum control landscape: a propagator approach

Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator. For bilinear quantum control problems, no general results are available to fully determine when this mapping is singular or not. In this paper we give suffcient conditions, in terms of elements of the evolution semigroup, for a trajectory to be non-singular. We identify two lists of "way-points" that, when reached, ensure the non-singularity of the control trajectory. It is found that under appropriate hypotheses one of those lists does not depend on the values of the coupling operator matrix

From Tensor Equations to Numerical Code -- Computer Algebra Tools for Numerical Relativity

In this paper we present our recent work in developing a computer-algebra tool for systems of partial differential equations (PDEs), termed "Kranc". Our work is motivated by the problem of finding solutions of the Einstein equations through numerical simulations. Kranc consists of Mathematica based computer-algebra packages, that facilitate the task of dealing with symbolic tensorial calculations and realize the conversion of systems of partial differential evolution equations into parallelized C or Fortran code.Comment: LaTeX llncs style, 9 pages, 1 figure, to appaer in the proceedings of "SYNASC 2004 - 6th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing", Timisoara, Romania, September 26-30 200

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.In the present paper we solve space-time fractional diffusion-wave equation with two space variables, using the matrix method. Here, in particular, we give solutions to classical diffusion and wave equations and fractional diffusion and wave equations with different combinations of time and space fractional derivatives. We also plot some graphs for these problems with the help of MATLAB routines

Perfectly Matched Layers in a Divergence Preserving ADI Scheme for Electromagnetics

For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 um the computational domain has dimensions roughly 5 orders of magnitude larger resulting in very large mesh sizes. The particles are confined to a small area of this domain only. To resolve the smallest scales close to the particles subgrids are envisioned. For reasons of stability the alternating direction implicit (ADI) scheme by D. N. Smithe et al. (J. Comput. Phys. 228 (2009) pp.7289-7299) for Maxwell equations has been adopted. At the boundary of the domain absorbing boundary conditions have to be employed to prevent reflection of the radiation. In this paper we show how the divergence preserving ADI scheme has to be formulated in perfectly matched layers (PML) and compare the performance in several scenarios.Comment: 8 pages, 6 figure