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On a Recovery Problem
(1995)SAM Research ReportThis paper concerns itself with the recovery of the coefficients, shifts and, where applicable, dilates of a given form f(\bfx)=∑j=1mcjG(\bfx−\bftj), or f(\bfx)=∑j=1mcjg(\bfaj⋅\bfx−bj),\bfx∈\RRn, where emf/em, emG/em and emg/em are known. That is, we provide a method that identifies the quantities $c_j$, $\bft_j$, $\bfa_j$ and $b_j$. In some cases we can even find emG/em given only emf/em and knowing that emf/em is of the above form.Report -
Eliminating the shortcomings of free datatype definitions
(1995)Technischer Bericht / Eidgenössische Technische Hochschule, Departement InformatikReport -
The Method of Transport for solving the Euler-equations
(1995)SAM Research ReportIn many technical applications it is necessary to compute a numerical solution of complex flow problems in several space dimensions. Most available codes split the multi-dimensional problem into several one-dimension\-al ones. Those are aligned with the cell interfaces of the underlying grid. In some of the applications, e.g.high Mach number flow, this approach does not work very well, since the physical properties of the model equations ...Report -
Decomposition of the multidimensional Euler equations into advection equations
(1995)SAM Research ReportBased on a genuine multi-dimensional numerical scheme, called Method of Transport, we derive a form of the compressible Euler-equations, capable of a linearization for any space dimension. This form allows a rigorous error analysis of the linearization error without the knowledge of the numerical method. The generated error can be eliminated by special correction terms in the linear equations. Hence, existing scalar high order methods can ...Report -
Radial Functions on Compact Support
(1995)SAM Research ReportIn this paper, radial basis functions that are compactly supported and give rise to positive definite interpolation matrices for scattered data are discussed. They are related to the well-known thin plate spline radial functions which are highly useful in applications for gridfree approximation methods. Also, encouraging approximation results for the compactly supported radial functions are shown.Report -
Stability of time discretization, Hurwitz determinants and order stars
(1995)SAM Research ReportWe shall review stability requirements for time discretizations of ordinary and partial differential equations. If a constant time step is used and the method involves more than two time levels stability is always related to the location of roots of a polynomial in circular or half plane regions. In several cases the coefficients of the polynomial depend on a real or complex parameter. Hurwitz determinants allow to create a fraction free ...Report -
Multidimensional schemes for nonlinear systems of hyperbolic conservation laws
(1995)SAM Research ReportMost commonly used schemes for unsteady multidimensional systems of hyperbolic conservation laws use dimensional splitting. In each coordinate direction a scheme for a one dimensional system is used. Such an approach does not take in account the infinitely many propagation directions which are present in a system in several space dimensions. In 1992 M. Fey introduced what he called the Method of Transport, MoT, for the Euler equations of ...Report -
Lagestabilität lückenloser Meterspurgleise in kleinen Bogenradien
(1995)IVT SchriftenreiheReport -
Fully Discrete Multiscale Galerkin BEM
(1995)SAM Research ReportWe analyze multiscale Galerkin methods for strongly elliptic boundary integral equations of order zero on closed surfaces in $R^3$. Piecewise polynomial, discontinuous multiwavelet bases of any polynomial degree are constructed explicitly. We show that optimal convergence rates in the boundary energy norm and in certain negative norms can be achieved with "compressed" stiffness matrices containing $O(N({\log N})^2)$ nonvanishing entries ...Report