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- RPI SCOREC - Technical Reports

is studied Our approach is motivated by the fact that i the effective stiffness matrix is well conditioned because of the stabilizing effect of the diagonally dominated mass matrix ii the dominance of the temporal error in implicit computations with large step size and iii the utilization of a class of iterative methods where the primary computational cost is associated with a construction of the preconditioner rather than with an

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=126 (2015-07-15)

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entities resulting from extremely small geometric model features is described The algorithm dramatically improves the quality of automatically generated meshes An automated incremental algorithm based on local mesh modifications is developed to correct acceptably distorted curvilinear mesh entities A novel decomposition of hierarchic shape functions based on mesh topological adjacency is developed that allows for the unified and consistent specification and evaluation of variable p order C finite element approximations over conforming meshes with mixed topology entities including line triangle quadrilateral tetrahedron hexahedron wedge and pyramid elements A general and efficient scheme for evaluation of higher order element level integrals is presented based on direct polynomial approximation of the integrand followed by use of precomputed exact values of the resulting polynomial integrals It is shown that to preserve the rate of convergence of the finite element solution error for second order elliptic boundary value problems using a p th order basis the integrand approximation must be at least accurate to order p 1 Blending schemes are used to construct mesh geometry mapping procedures that conform exactly to the domain boundary definition within a geometric modeling system The concept of permutation of element parametric coordinates is developed to identify symmetries in

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=127 (2015-07-15)

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Software Framework for Mechanism Based Design of Composite Structures Year 1997 Journal Ceramic Engineering and Science Proceedings Volume 18 4 Pages 307 314 Editor Abstract A software framework supporting mechanism based design of high temperature composite structures is described The framework extends material property databases by allowing the investigation and simulation of small scale behaviors which cause full scale effects The framework integrates a full range of modeling processes including

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=128 (2015-07-15)

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M S Shephard Title Modeling and Adaptive Numerical Techniques for Oxidation of Ceramic Composites Year 1997 Pages Editor Abstract We develop a mathematical model for the oxidation of silicon carbide in a crack or pore The model consists of a

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=129 (2015-07-15)

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finite elements on curved three dimensional domains Specific options to account for domain geometry information during element level computation are identified Accuracy requirements on the geometry related approximations to preserve the optimal rate of finite element error convergence for second order elliptic boundary value problems are given An element geometric mapping scheme based on blending the exact shape of the domain boundary is described that can either be used directly

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=130 (2015-07-15)

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laws are solved by a local Galerkin finite element procedure with adaptive space time mesh refinement and explicit time integration The Courant stability condition is used to select smaller time steps on smaller elements of the mesh thereby greatly increasing efficiency relative to methods having a single global time step Processor load imbalances introduced at adaptive enrichment steps are corrected by using traversals of an octree representing a spatial decomposition

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=131 (2015-07-15)

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R Arabnia ISBN 0 9648666 8 4 Abstract This paper describes two predictive load balancing schemes designed for use with parallel adaptive finite element methods We also provide an overview of data structures suitable for distributed storage of finite element mesh data as well as software designed for mesh adaptation and load balancing During the course of a parallel computation processor load imbalances are introduced at adaptive enrichment steps The

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=132 (2015-07-15)

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problem Since these idealizations are introduced to make solving the problem tractable due to constraints on either problem size and or solution time it is necessary to understand their effect on the solution obtained and to have procedures to reduce the errors to an acceptable level with respect to the reason the analysis is being performed Understanding the effects of idealizations requires a more complete definition of the problem than

Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=133 (2015-07-15)

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