Parallel EFG algorithm for heat transfer problems

At present, meshless element free Galerkin (EFG) method is being successfully applied in the areas such as solid mechanics, fracture mechanics and thermal. Being a meshless method, it has many advantages over finite element method. One big hurdle with the wide implementation of this method is its computational cost. Therefore, in this paper, a parallel algorithm is proposed for the EFG method. The parallel code has been written in FORTRAN language using MPI message passing library and executed on a four node (eight processors) MIMD type, distributed memory 'PARAM 10000' parallel computer. The total time, communication time, speedup and efficiency have been estimated for a three-dimensional heat transfer problem to validate the proposed algorithm. For eight processors, the speedup and efficiency are obtained to be 4.66 and 58.22%, respectively, for a data size of 1320 nodes.

[1]  Genki Yagawa,et al.  Large-scale parallel flow analysis based on free mesh method: a virtually meshless method , 1999 .

[2]  Genki Yagawa,et al.  Performance study of the domain decomposition method with direct equation solver for parallel finite element analysis , 1996 .

[3]  Michael Griebel,et al.  A Particle-Partition of Unity Method-Part IV: Parallelization , 2003 .

[4]  Ted Belytschko,et al.  An introduction to programming the meshless Element F reeGalerkin method , 1998 .

[5]  Duc T. Nguyen,et al.  A tridiagonal solver for massively parallel computers , 1998 .

[6]  M. Kreienmeyer,et al.  Parallel implementation of the boundary element method for linear elastic problems on a MIMD parallel computer , 1995 .

[7]  T. Belytschko,et al.  DYNAMIC FRACTURE USING ELEMENT-FREE GALERKIN METHODS , 1996 .

[8]  Dipankar K. Ghosh,et al.  A parallel programming environment for adaptive p-version finite element analysis , 1998 .

[9]  Ganesh Thiagarajan,et al.  Parallelization strategies for element-by-element preconditioned conjugate gradient solver using high-performance Fortran for unstructured finite-element applications on linux clusters , 2002 .

[10]  Ravi Prakash,et al.  The Element Free Galerkin Method in Three Dimensional Steady State Heat Conduction , 2002, Int. J. Comput. Eng. Sci..

[11]  Vlatko Cingoski,et al.  Element-free Galerkin method for electromagnetic field computations , 1998 .

[12]  Robert Ferraro,et al.  Parallel computation for natural convection , 1997 .

[13]  I. Singh,et al.  HEAT TRANSFER ANALYSIS OF TWO-DIMENSIONAL FINS USING MESHLESS ELEMENT FREE GALERKIN METHOD , 2003 .

[14]  Kent T. Danielson,et al.  Nonlinear dynamic finite element analysis on parallel computers using FORTRAN 90 and MPI 1 This pape , 1998 .

[15]  T. Belytschko,et al.  Crack propagation by element-free Galerkin methods , 1995 .

[16]  P. J. Coelho,et al.  Parallelization of the finite volume method for radiation heat transfer , 1999 .

[17]  T. Belytschko,et al.  Element-free galerkin methods for static and dynamic fracture , 1995 .

[18]  D. Medina,et al.  Three-dimensional simulations of impact induced damage in composite structures using the parallelized SPH method , 2000 .

[19]  C. S. Ierotheou,et al.  The implementation of an aeronautical CFD flow code onto distributed memory parallel systems , 2000 .

[20]  Asif Usmani,et al.  Finite element analysis of solidification using object-oriented and parallel techniques , 1997 .

[21]  Ted Belytschko,et al.  A coupled finite element-element-free Galerkin method , 1995 .

[22]  Barry Hilary Valentine Topping,et al.  Parallel finite element analysis using Jacobi-conditioned conjugate gradient algorithm , 1996 .

[23]  P. Bouillard,et al.  Element-Free Galerkin solutions for Helmholtz problems: fomulation and numerical assessment of the pollution effect , 1998 .

[24]  T. Belytschko,et al.  Analysis of thin shells by the Element-Free Galerkin method , 1996 .

[25]  Graham F. Carey,et al.  Parallel conjugate gradient performance for least-squares finite elements and transport problems , 1998 .

[26]  Chi Leung Welkin Li,et al.  A PARALLEL COMPUTING SOLUTION OF HEAT AND MOISTURE TRANSFER IN UNSATURATED SOIL , 1996 .

[27]  Mark A. Christon,et al.  Multi-scale meshfree parallel computations for viscous, compressible flows , 2000 .

[28]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[29]  T. Belytschko,et al.  A new implementation of the element free Galerkin method , 1994 .

[30]  Guangyao Li,et al.  Element‐free Galerkin method for contact problems in metal forming analysis , 2001 .

[31]  Ted Belytschko,et al.  Analysis of thin plates by the element-free Galerkin method , 1995 .

[32]  Ted Belytschko,et al.  Element-free Galerkin method for wave propagation and dynamic fracture , 1995 .

[33]  Mark A Fleming,et al.  Smoothing and accelerated computations in the element free Galerkin method , 1996 .

[34]  Xiaohu Sun,et al.  A three-level parallelization of spatial direct numerical simulation , 1998 .