On the Parallelization of Self-Adaptive hp-Finite Element Methods Part I. Composite Programmable Graph GrammarModel

The paper present the composite programmable (CP) graph grammar model of the selfadaptive hp Finite Element Method (hp-FEM) algorithm. The model incorporates the process of the initial mesh generation, direct solver execution, as well as mesh transformations resulting from selectedoptimal hp refinements. The computational mesh is represented by the CP-graph. The operations performed over the mesh are expressed by the graph grammar productions. The graph grammar model allows for the definition of the computational tasks for the Partitioning, Communication, Agglomeration and Mapping (PCAM) method of the parallelization of the self-adaptive hp-FEM algorithm.

[1]  Anna Paszynska,et al.  Graph Transformations for Modeling Parallel hp-Adaptive Finite Element Method , 2007, PPAM.

[2]  Carlos Torres-Verdín,et al.  Two-Dimensional High-Accuracy Simulation of Resistivity Logging-While-Drilling (LWD) Measurements Using a Self-Adaptive Goal-Oriented hp Finite Element Method , 2006, SIAM J. Appl. Math..

[3]  D. Pardo,et al.  Simulations of 3D DC borehole resistivity measurements with a goal-oriented hp finite-element method. Part II: through-casing resistivity instruments , 2008 .

[4]  Mark S. Shephard,et al.  a General Topology-Based Mesh Data Structure , 1997 .

[5]  Maciej Paszynski.  Agents Based Hierarchical Parallelization of Complex Algorithms on the Example of hp Finite Element Method , 2007, International Conference on Computational Science.

[6]  Maciej Paszynski,et al.  Parallel, fully automatic hp-adaptive 3D finite element package , 2006, Engineering with Computers.

[7]  Carlos Torres-Verdín,et al.  Simulation of 3D Resistivity Logging Measurements with a Parallel Implementation of 2D hp‐Adaptive Goal‐Oriented Finite Element Method , 2007 .

[8]  L. Demkowicz,et al.  SIMULATION OF RESISTIVITY LOGGING-WHILE-DRILLING (LWD) MEASUREMENTS USING A SELF-ADAPTIVE GOAL-ORIENTED HP FINITE ELEMENT METHOD , 2022 .

[9]  Maciej Paszynski.  Performance of Multi Level Parallel Direct Solver for hpFinite Element Method , 2007, PPAM.

[10]  I. Babuska,et al.  Rairo Modélisation Mathématique Et Analyse Numérique the H-p Version of the Finite Element Method with Quasiuniform Meshes (*) , 2009 .

[11]  L. Demkowicz.  One and two dimensional elliptic and Maxwell problems , 2006 .

[12]  Maciej Paszynski.  On the Parallelization of Self-Adaptive hp-Finite Element Methods Part II. Partitioning Communication Agglomeration Mapping (PCAM) Analysis , 2009, Fundam. Informaticae.

[13]  Leszek Demkowicz,et al.  Verification of goal-oriented HP-adaptivity , 2005 .

[15]  B. Guo,et al.  The hp version of the finite element method Part 1 : The basic approximation results , 2022 .

[16]  Maciej Paszyński,et al.  Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications , 2007 .

[17]  Maciej Paszyński,et al.  On the Modeling of Step-and-Flash Imprint Lithography using Molecular Statics Models , 2005 .

[18]  I. Babuška,et al.  The h-p version of the finite element method , 1986 .

[19]  Robert Schaefer,et al.  Efficient Adaptive Strategy for Solving Inverse Problems , 2007, International Conference on Computational Science.

[20]  Ian T. Foster,et al.  Designing and building parallel programs - concepts and tools for parallel software engineering , 1995 .

[21]  D. Pardo,et al.  A 2D and 3D hp-Finite Element Method for Simulation of Through Casing Resistivity Logging Instruments , 2006, 2006 IEEE Antennas and Propagation Society International Symposium.

[22]  Maciej Paszynski,et al.  Parallel, fully automatic hp-adaptive 3D finite element package , 2007, Engineering with Computers.

[23]  Leszek Demkowicz,et al.  Parallel, fully automatic hp-adaptive 2d finite element package , 2006 .

[25]  A. Peirce.  Computer Methods in Applied Mechanics and Engineering , 2010 .

[26]  Carlos Torres-Verdín,et al.  Parallel hp-Finite Element Simulations of 3D Resistivity Logging Instruments , 2006, ISPE CE.

[27]  David Pardo,et al.  A self-adaptive goal-oriented hp-finite element method with electromagnetic applications. Part II: Electrodynamics , 2007 .

[28]  Maciej Paszynski.  The Application of Agents to Parallel Mesh Refinements in Domain Decomposition Based Parallel Fully Automatic hp Adaptive Finite Element Codes , 2006, International Conference on Computational Science.

[29]  David Pardo,et al.  Simulation of 3D DC Borehole Resistivity Measurements with a Goal- Oriented hp Finite-Element Method. Part I: Laterolog and LWD , 2007 .