Higher-order intergrid transfer operators used within cell-centered multigrid can improve the convergence properties of the multigrid method compared to low-order operators. In this thesis those operators are analyzed and incorporated into the LSE (linear systems of equation) module of the waLBerla software framework. The aim is to provide a solver for Poisson and Poisson-Boltzmann partial di e...

We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial di erential equations. We introduce and prove a veri cation theorem which provides a su cient condition for optimality. Moreover we prove suband superoptimality principles of dynamic programming and present an explicit construction of -optimal ...

ly u t is nothing more than an element in a Banach space B and this leaves room for applications to a wide variety of problems in di erential equations As in the examples above B might be L and A might be x or x and homogeneous boundary conditions could be included by restricting B appropriately More generally u t could be an vector valued function of multiple space variables The next step is t...

Abstract. We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and constant coe cients on the half line. Our method results in a matrix equation of special structure which can be solved in O(N logN) operations. We also take advantage of recurrence relations for the generalize...

We describe herein the parallel implementation of the Bi-CGSTAB method with a block Red-Black Gauss-Seidel (RBGS) preconditioner applied to the systems of linear algebraic equations that arise from the Hermite collocation discretization of partial di erential equations in two spatial dimensions. The method is implemented on the Cray T3E, a parallel processing supercomputer. Speedup results are ...

For linear di erential algebraic equations of tractability index 1 the notion of the adjoint equation is analysed in full detail. Its solvability is shown at the lowest possible smoothness. The fundamental matrices of both equations are de ned and their relationships are characterized.

In this paper, decision{feedback di erential detection (DF{DD) ofM{ary di erential phase{shift keying (MDPSK) signals, which has been introduced previously for the additive white Gaussian noise (AWGN) channel by Leib et al. [1] and Edbauer [2], is extended to at Rayleigh fading channels. The DF{DD metric is derived from the multiple{symbol detection (MSD) metric and for error{free feedback an e...

We present an algorithm for the solution of a nontrivial coupled system of algebraic Riccati equations appearing in risk sensitive control problems. Moreover we use comparison methods to derive non blow up conditions for the solutions of a corresponding terminal value problem for coupled systems of Riccati di erential equations.

In this paper we present some results about analytic machines regarding the power of computations over Q or R solutions of di erential equations and the stability problem of dynamical systems We rst explain the machine model which is a kind of Blum Shub Smale machine enhanced by in nite convergent computations Next we com pare the computational power of such machines over the elds Q and R showi...