The distributed relaxation method for the Stokes problem has been advertised as an adequate change of variables that leads to a lower triangular systemwith Laplace operators on the main diagonal for which multigrid methods are very efficient. We show that under high regularity of the Laplacian, the transformed system admits almost block-lower triangular form.We analyze the distributed relaxatio...

We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-toone mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to an equivalent problem for an operator with variable coefficients. Taking advantage of the simple geometry we separate variables by means of the F...

The numerical study of exterior acoustics problems is usually carried out in the frequency domain. Finite element analyses often require the solution of large scale algebraic linear systems. For very large problems, sometimes the time domain is used. Implicit time integration requires linear system solves, but these are often far easier than those from the frequency domain. This paper shows a c...

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Dynamische Prozesse, bei welchen die Systemgrößen eine kontinuierliche Abhängigkeit vom Ort aufweisen, können durch partielle Differentialgleichungen beschrieben werden. Durch die Anwendung der Laplace-Transformation werden diese Gleichungen in gewöhnliche Differentialgleichungen überführt und anschließend im Bildbereich gelöst. Die Lösung kann durch Manipulation in eine in den gesuchten Parame...

In this paper we present and compare two diier-ent approaches for the transient solution of Markov regenerative stochastic Petri Nets: the method based on Markov regenerative theory and the method of supplementary variables. In both cases the equations that govern the marking process of the non-Markovian stochastic Petri net are presented and then solved either in time-domain or using a Laplace...

In this paper we introduce Hilbert spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced transformation, the Gauss map, respectively. By means of a suitable operator-valued power series we are able to study simultaneously the spectrum of both these operators along with the analytic pr...

In this paper a new approach to rational discrete-time approximations to continuous fractional-order systems of the form 1/(s+p) is proposed. We will show that such fractional-order LTI system can be decomposed into subsystems. One has the classic behavior and the other is similar to a Finite Impulse Response (FIR) system. The conversion from continuous-time to discrete-time systems will be don...

Renormalization Group Fixed Point Hans Koch 1 Department of Mathematics, University of Texas at Austin Austin, TX 78712 Peter Wittwer 2 D epartement de Physique Th eorique, Universit e de Gen eve Gen eve, CH 1211 Abstract. We prove that the Renormalization Group transformation for the Laplace transform of the d = 3 Dyson{Baker hierarchical model has a nontrivial entire analytic xed point whose ...

The C library libkww provides functions to compute the Kohlrausch–Williams– Watts function, i.e., the Laplace–Fourier transform of the stretched (or compressed) exponential function exp(−t) for exponents β between 0.1 and 1.9 with double precision. Analytic error bounds are derived for the low and high frequency series expansions. For intermediate frequencies, the numeric integration is enormou...