A parallel multigrid method for history-dependent elastoplasticity computations

International audienceThis paper presents an adaptive refinement strategy based on a hierarchical element subdivision dedicated to modeling elastoplastic materials in transient dynamics. At each time step, the refinement is automatic and starts with the calculation of the solution on a coarse mesh. Then, an error indicator is used to control the accuracy of the solution and a finer localized mesh is created where the user prescribed accuracy is not reached. A new calculation is performed on this new mesh using the non linear ``Full Approximation Scheme'' (FAS) multigrid strategy. Applying the error indicator and the refinement strategy recursively, the optimal mesh is obtained. This mesh verifies the error indicator on the whole structure. The multigrid strategy is used for two purposes. First, it optimizes the computational cost of the solution on the finest localized mesh. Second, it ensures information transfer amongst the different hierarchical meshes. A standard time integration scheme is used and the mesh is reassessed at each time step

Section: Principlementioning

confidence: 99%

Multigrid solver with automatic mesh refinement for transient elastoplastic dynamic problems

Biotteau¹,

Gravouil²,

Lubrecht³

et al. 2010

“…Algebraic multigrid methods are unstructured by deÿnition and work only with the graphs of the 'grids' and usually use the actual values in the operator matrices to construct the grid transfer operators. We are aware of two classes of multigrid methods that show promise for elasticity problems: non-nested geometric [4][5][6][7][8][9] and aggregation algebraic based on the rigid body modes [10][11][12]. Another class of algebraic methods that show promise, but have not yet been shown to be practical for large-scale elasticity problems, are element base aggregation methods (all other aggregation methods discussed in this paper are nodal aggregation methods), see Henson [13] and the references therein.…”

Section: Unstructured Multigrid Methodsmentioning

confidence: 99%

“…This problem is run with a 560 block Jacobi preconditioner for the PCG smoother. This problem has a condition number of about 1:0×10 9 and Plate 3 shows the deformed mesh with the ÿrst principle stress of a 22 000 dof version of this problem. Table IV shows the sizes of the coarse grids along with the iteration counts for this problem.…”

Section: Wingmentioning

confidence: 99%

See 1 more Smart Citation

Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics

Adams

2002

SUMMARYMultigrid has been a popular solver method for ÿnite element and ÿnite di erence problems with regular grids for over 20 years. The application of multigrid to unstructured grid problems, in which it is often di cult or impossible for the application to provide coarse grids, is not as well understood. In particular, methods that are designed to require only data that are easily available in most ÿnite element applications (i.e. ÿne grid data), constructing the grid transfer operators and coarse grid operators internally, are of practical interest. We investigate three unstructured multigrid methods that show promise for challenging problems in 3D elasticity: (1) non-nested geometric multigrid, (2) smoothed aggregation, and (3) plain aggregation algebraic multigrid. This paper evaluates the e ectiveness of these three methods on several unstructured grid problems in 3D elasticity with up to 76 million degrees of freedom.

“…These computations can account for as much as 95% of the total CPU time [22]. Therefore, this operation has to be implemented in the most efficient way.…”

Section: Matrix-vector Multiplicationsmentioning

confidence: 99%

A distributed memory parallel implementation of the multigrid method for solving three‐dimensional implicit solid mechanics problems

Namazifard

Parsons

2004

SUMMARYWe describe the parallel implementation of a multigrid method for unstructured finite element discretizations of solid mechanics problems. We focus on a distributed memory programming model and use the MPI library to perform the required interprocessor communications. We present an algebraic framework for our parallel computations, and describe an object-based programming methodology using Fortran90. The performance of the implementation is measured by solving both fixed-and scaled-size problems on three different parallel computers (an SGI Origin2000, an IBM SP2 and a Cray T3E). The code performs well in terms of speedup, parallel efficiency and scalability. However, the floating point performance is considerably below the peak values attributed to these machines. Lazy processors are documented on the Origin that produce reduced performance statistics. The solution of two problems on an SGI Origin2000, an IBM PowerPC SMP and a Linux cluster demonstrate that the algorithm performs well when applied to the unstructured meshes required for practical engineering analysis.