An object-oriented framework for finite element analysis based on a compact topological data structure

This paper describes an ongoing work in the development of a finite element analysis system, called TopFEM, based on the compact topological data structure, TopS [1,2]. This new framework was written to take advantage of the topological data structure together with object-oriented programming concepts to handle a variety of finite element problems, spanning from fracture mechanics to topology optimization, in an efficient, but generic fashion. The class organization of the TopFEM system is described and discussed within the context of other frameworks in the literature that share similar ideas, such as GetFEM++, deal.II, FEMOOP and OpenSees. Numerical examples are given to illustrate the capabilities of TopS attached to a finite element framework in the context of fracture mechanics and to establish a benchmark with other implementations that do not make use of a topological data structure.

[1]  Z. Gaspar,et al.  Addenda and corrigenda to: (1) “Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics" and (2) “On design- dependent constraints and singular topologies" (Vol. 21, No. 2, 2001, pp. 90–108; 164–172) , 2002 .

[2]  Jianhu Nie,et al.  Development of an object-oriented finite element program with adaptive mesh refinement for multi-physics applications , 2010, Adv. Eng. Softw..

[3]  Peter L. Williams.  Visibility-ordering meshed polyhedra , 1992, TOGS.

[4]  Glaucio H. Paulino,et al.  A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes , 2008, Engineering with Computers.

[5]  Glaucio H. Paulino,et al.  Adaptive dynamic cohesive fracture simulation using nodal perturbation and edge‐swap operators , 2010 .

[6]  Laxmikant V. Kalé,et al.  ParFUM: a parallel framework for unstructured meshes for scalable dynamic physics applications , 2006, Engineering with Computers.

[7]  G. H. Paulino,et al.  A methodology for adaptive finite element analysis: Towards an integrated computational environment , 1999 .

[8]  G. Rozvany.  Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics , 2001 .

[9]  Mark S. Shephard,et al.  Efficient distributed mesh data structure for parallel automated adaptive analysis , 2006, Engineering with Computers.

[10]  Jean-François Remacle,et al.  Parallel Algorithm Oriented Mesh Database , 2002, Engineering with Computers.

[11]  T. Zimmermann,et al.  Object-oriented finite elements IV. Symbolic derivations and automatic programming of nonlinear formulations , 2001 .

[12]  Glaucio H. Paulino,et al.  Computational implementation of the PPR potential-based cohesive model in ABAQUS: Educational perspective , 2012 .

[13]  Thomas Zimmermann,et al.  Object-oriented finite element programming: I: Governing principles , 1992 .

[14]  Glaucio H. Paulino,et al.  A unified potential-based cohesive model of mixed-mode fracture , 2009 .

[15]  Thomas Zimmermann,et al.  Object-oriented finite element in programming: II: A prototype program in Smalltalk , 1992 .

[16]  William Gropp,et al.  Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries , 1997, SciTools.

[17]  Yuan Zheng.  Object-Oriented Finite Element Programming , 2000 .

[18]  O. Schenk,et al.  ON FAST FACTORIZATION PIVOTING METHODS FOR SPARSE SYMMETRI C INDEFINITE SYSTEMS , 2006 .

[19]  T. Zimmermann,et al.  Object-oriented finite elements III. Theory and application of automatic programming , 1998 .

[20]  Glaucio H. Paulino,et al.  A Unified Library of Nonlinear Solution Schemes , 2011 .

[21]  Michael H. Scott,et al.  Nonlinear Finite-Element Analysis Software Architecture Using Object Composition , 2010, J. Comput. Civ. Eng..

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

[23]  Timothy A. Davis,et al.  The university of Florida sparse matrix collection , 2011, TOMS.

[24]  Gregory L. Fenves,et al.  An object-oriented software design for parallel structural analysis , 2000 .

[25]  Glaucio H. Paulino,et al.  ParTopS: compact topological framework for parallel fragmentation simulations , 2009, Engineering with Computers.

[26]  ScienceDirect,et al.  Advances in engineering software , 2008, Adv. Eng. Softw..

[27]  Luiz Fernando Martha,et al.  An object-oriented framework for finite element programming , 2002 .

[28]  Glaucio H. Paulino,et al.  A compact adjacency‐based topological data structure for finite element mesh representation , 2005 .

[29]  Gregory R. Miller,et al.  An algorithmic framework for flexible finite element-based structural modeling , 1996 .

[30]  Jean-François Remacle,et al.  An algorithm oriented mesh database , 2003, IMR.

[31]  Daniel Ruiz,et al.  CFD Parallel Simulation Using Getfem++ and Mumps , 2010, Euro-Par.

[32]  Martin Kronbichler,et al.  Algorithms and data structures for massively parallel generic adaptive finite element codes , 2011, ACM Trans. Math. Softw..

[33]  G. Paulino,et al.  Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces , 2011 .

[34]  Jaroslav Mackerle,et al.  Object-oriented programming in FEM and BEM: a bibliography (1990-2003) , 2004 .

[35]  Gregory L. Fenves,et al.  Object-oriented finite element programming: frameworks for analysis, algorithms and parallel computing , 1997 .

[36]  Carsten Burstedde,et al.  p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees , 2011, SIAM J. Sci. Comput..

[37]  Timothy A. Davis,et al.  A combined unifrontal/multifrontal method for unsymmetric sparse matrices , 1999, TOMS.

[38]  Rao V. Garimella,et al.  Mesh data structure selection for mesh generation and FEA applications , 2002 .

[39]  Glaucio H. Paulino,et al.  Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture , 2012 .

[40]  Kevin Weiler.  Topological Structures for Geometric Modeling , 1986 .

[41]  Glaucio H. Paulino,et al.  Efficient Handling of Implicit Entities in Reduced Mesh Representations , 2005, J. Comput. Inf. Sci. Eng..

[42]  T. Zimmermann,et al.  Object-oriented finite elements I. Principles of symbolic derivations and automatic programming , 1996 .

[43]  Glaucio H. Paulino,et al.  Application of layout and topology optimization using pattern gradation for the conceptual design of buildings , 2011 .

[44]  T. Zimmermann,et al.  Object-oriented finite elements II. A symbolic environment for automatic programming , 1996 .

[45]  Timothy A. Davis,et al.  Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method , 2004, TOMS.

[46]  Glaucio H. Paulino,et al.  Topology optimization for braced frames: Combining continuum and beam/column elements , 2012 .

[47]  Surendra P. Shah,et al.  Mixed‐Mode Fracture of Concrete Subjected to Impact Loading , 1990 .

[48]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[49]  Timothy A. Davis,et al.  A column pre-ordering strategy for the unsymmetric-pattern multifrontal method , 2004, TOMS.

[50]  Thomas Zimmermann,et al.  Object-oriented finite element programming: III. An efficient implementation in C++ , 1993 .

[51]  Joseph S. B. Mitchell,et al.  Fast Polyhedral Cell Sorting for Interactive Rendering of Unstructured Grids , 1998, Comput. Graph. Forum.

[52]  Timothy A. Davis,et al.  An Unsymmetric-pattern Multifrontal Method for Sparse Lu Factorization , 1993 .

[53]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2002, Future Gener. Comput. Syst..