230 research outputs found

    Grid generation for the solution of partial differential equations

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    A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given

    Glosarium Matematika

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    273 p.; 24 cm

    Resolving non‐symmetry in flows via subdomain shifts

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    In this study, non‐symmetric flow problems are modeled by selecting subdomains and shifting them in such a way that the symmetry is recovered. As a result, the domains are made of simple grid structures and re‐generation of mesh is avoided. Three test problems with various decomposition characteristics, namely, translation, rotation and deformation are selected, and they are analyzed in different flow regimes. To study the internal flow between eccentric cylinders, two cylindrical concentric subdomains are considered, one translated relative to the other. Hence, a simple polar‐coordinates mesh can be utilized instead of generating a mesh for the solution domain between the eccentric cylinders of the original problem. External flow around a curvature tube is studied shifting the subdomain around the object in rotation, relative to the outer domain thus avoiding a re‐generation of the mesh as the angle‐of‐attack changes. A third example involves deformation of an object exposed to natural convection, and the shifting of the domain facilitates the iteration process as the object deflects. Systems of nonlinear equations are solved within Newton‐Krylov framework using the matrix‐free approach. Geometrical and physical parameters are used to improve the solution process. Several results are provided to show the applicability of proposed method. First published online: 09 Jun 201

    Glosarium Matematika

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    Adaptive Discontinuous Galerkin Methods for Variational Inequalities with Applications to Phase Field Models

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    Solutions of variational inequalities often have limited regularity. In particular, the nonsmooth parts are local, while other parts of the solution have higher regularity. To overcome this limitation, we apply hp-adaptivity, which uses a combination of locally finer meshes and varying polynomial degrees to separate the different features of the the solution. For this, we employ Discontinuous Galerkin (DG) methods and show some novel error estimates for the obstacle problem which emphasize the use in hp-adaptive algorithms. Besides this analysis, we present how to efficiently compute numerical solutions using error estimators, fast algebraic solvers which can also be employed in a parallel setup, and discuss implementation details. Finally, some numerical examples and applications to phase field models are presented

    [Research activities in applied mathematics, fluid mechanics, and computer science]

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    This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995

    The Sixth Copper Mountain Conference on Multigrid Methods, part 2

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    The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth
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