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Solution of the 3D-Helmholtz equation in exterior domains of arbitrary shape using HP-finite infinite elements
(1996)SAM Research ReportThis work is devoted to a convergence and performance study of finite-infinite element discretizations for the Helmholtz equation in exterior domains of arbitrary shape. The proposed approximation applies to arbitrary geometries, combining an emhp/em FE discretization between the object and a surrounding sphere and an {\em hp} Infinite Element (IE) discretization outside the sphere with a spectral-like representation (resulting from the ...Report -
Stability analysis for the method of transport
(1996)SAM Research ReportIn this paper, we provide analytical stability estimates for the method of transport. We first prove stability of the second-order method of transport applied to the linear advection equation with constant coefficient in one dimension by using the von Neumann method and with the positive operator technique. In a second step, we extend the proof to the linear advection equation with variable coefficient. Finally, we investigate and compare ...Report -
GIPSY: Generating Integrated Process Support Systems
(1996)TIK ReportCooperative software engineering requires integration of a distributed and heterogeneous world of actors and resources. Component technology will augment integration problems due to distributed development of large numbers of interoperating components. Extensible Attribute Grammars (EAG) are used for the specification and generation of highly integrated tool components that support the software process. Tool components are plugged into a ...Report -
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Contour Plots of Analytic Functions
(1996)SAM Research ReportThis is a tutorial on generating contour lines of an analytic function $f(z)$. The emphasis is on using mathematical software (MATLAB, to a lesser extent MAPLE) for implementing the algorithms, and efficient programs together with explanations are presented. Two different approaches are suggested: (1) generating level lines as contours of, e.g., constant modulus or constant phase of the function $f(z)$, (2) setting up and numerically ...Report -
The Application of Object Oriented Methods to Boundary Element
(1996)SAM Research ReportIn this paper we present the design of a class library to support the development of software for boundary elements. We discuss the extensibility and reusability of the library and give an example of its application.Report -
Asymptotically Optimal Approximation and Numerical Solutions of Differential Equations
(1996)SAM Research ReportAn optimal finite difference method for the numerical solution of the Cauchy problem for a given partial differential equation is, by definition, the scheme that minimises the local truncation error after one step. In this paper we conduct a study of certain extremal problems that are closely related to optimal finite difference schemes for finding numerical solutions of such problems.Report -
Functional Equations Related to the Iteration of Functions
(1996)SAM Research ReportCertain systems of functional equations related to the iteration of functions with a fixed point are considered. We construct smooth solutions in terms of expansions about the fixed point. In a particular example taken from an intuitive geometric situation the solution is obtained explicitly as a convergent Taylor series. Particular attention is given to the question of selecting distinguished solutions from an infinity of possible ...Report -
M.J.D. Powell's work in univariate and multivariate approximation theory and his contribution to optimization
(1996)SAM Research ReportSince 1966, exactly 30 years ago, Mike Powell has published more than 40 papers in approximation theory, initially mostly on univariate approximations and then, focussing especially on radial basis functions, also on multivariate methods. A highlight of his work is certainly his book {\it Approximation theory and methods}, published by CUP in 1981, that summarizes and extends much of his work on $\ell_1$, $\ell_2$, $\ell_\infty$ theory ...Report