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Fully Discrete hp-Finite Elements: Fast Quadrature
(1999)SAM Research ReportA fully discrete hp finite element method is presented. It combines the features of the standard hp finite element method (conforming Galerkin Formulation, variable order quadrature schemes, geometric meshes, static condensation) and of the spectral element method (special shape functions and spectral quadrature techniques). The speed-up (relative to standard hp elements) is analyzed in detail both theoretically and computationally .Report -
Fuzzy decision diagrams for the representation, analysis, and optimization of rule bases
(1999)TIK ReportWhen no expert knowledge is available, fuzzy if-then rules may be extracted from examples of performance of a system. For this, an a priori decision on the number of linguistic terms of the linguistic variables may be required. This may induce a "rigid granularity", usually finer than that actually required by the system. Fuzzy decision diagrams (FuDDs) are introduced as an efficient data structure to represent fuzzy rule bases and to ...Report -
The hp-Version of the Streamline Diffusion Finite Element Method in Two Space Dimensions
(1999)SAM Research ReportThe Streamline Diffusion Finite Element Method (SDFEM) for a two dimensional convection-diffusion problem is analyzed in the context of the hp-version of the Finite Element Method (FEM). It is proved that the appropriate choice of the SDFEM parameters leads to stable methods on the class of "boundary layer meshes" which may contain anisotropic needle elements of arbitrarily high aspect ratio. Consistency results show that the use of such ...Report -
Quality-of-Service based assessment of synchronization algorithms
(1999)TIK ReportIn this report we present a Quality-of-Service based methodology to assess synchronization algorithms. The methodology comprises two steps: Firstly, synchrinization algorithms are analized based on a defined set of QoS parameters for synchronization algorithms. Secondly, the analysis results are evaluated. The assessment methodology is validated by applying it to two well-known algorithms. Analysis and evaluation results as well as the ...Report -
hp-FEM for Hyperbolic Problems
(1999)SAM Research ReportThis paper is devoted to the a priori and a posteriori error analysis of the hp-version of the discontinuous Galerkin finite element method for partial differential equations of hyperbolic and nearly-hyperbolic character. We consider second-order partial differential equations with nonnegative characteristic form, a large class of equations which includes convection-dominated diffusion problems, degenerate elliptic equations and second-order ...Report -
Numerical integration of differential algebraic systems and invariant manifolds
(1999)SAM Research ReportThe dynamics of a differential algebraic equation takes place on a lower dimensional manifold in phase space. Applying a numerical integration scheme, it is natural to ask if and how this geometric property is preserved by the discrete dynamical system. In the index-1 case answers to this question are obtained from the singularly perturbed case treated in [6] for Runge-Kutta methods and in [7] for linear multistep methods. As main result, ...Report -
Optimized software synthesis for DSP using randomization techniques
(1999)TIK ReportThis paper addresses the problem of trading-off between the minimization of program and data memory requirements of single-processor implementations of dataflow programs. Based on the formal model of synchronous data flow (SDF) graphs, so called single appearance schedules are known to be program-memory optimal. Among these schedules, buffer memory schedules are investigated and explored based on a two-step approach: (1) An Evolutionary ...Report -
hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form
(1999)SAM Research ReportWe develop the error analysis for the hp-version of a discontinuous finite element approximation to second-order partial differential equations with nonnegative characteristic form. This class of equations includes classical examples of second-order elliptic and parabolic equations, first-order hyperbolic equations, as well as equations of mixed type. We establish an a priori error bound for the method which is of optimal order in the ...Report -
Exponential Convergence in a Galerkin Least Squares hp-FEM for Stokes Flow
(1999)SAM Research ReportA stabilized hp-Finite Element Method (FEM) of Galerkin Least Squares (GLS) type is analyzed for the Stokes equations in polygonal domains. Contrary to the standard Galerkin FEM, this method admits equal-order interpolation in the velocity and the pressure, which is very attractive from an implementational point of view. In conjunction with geometrically refined meshes and linearly increasing approximation orders it is shown that thehp-GLSFEM ...Report -
Advanced boundary element algorithms
(1999)SAM Research ReportWe review recent algorithmic developments in the boundary element method (BEM) for large scale engineering calculations. Two classes of algorithms, the clustering and the wavelet-based schemes are compared. Both have $O(N(\log N)^a)$ complexity with some small $a \ge 0$ and allow in-core simulations with up to $N = O(10^6)$ DOF on the boundary on serial workstations. Clustering appears more robust for complex surfaces.Report