FINITE ELEMENT METHODS AND SYSTEMS

摘要

The computational efficiency of Finite Element Methods (FEM) on parallel architectures is typically severely limited by sparse iterative solvers. Standard iterative solvers are based on sequential steps of global algebraic operations, which limit their parallel efficiency, and prior art techniques exploit sophisticated programming techniques tailored to specific CPU architectures to improve performance. The inventors present a FEM Multigrid Gaussian Belief Propagation (FMGaBP) technique that eliminates global algebraic operations and sparse data-structures based upon reformulating the variational FEM into a probabilistic inference problem based upon graphical models. Further, the inventors present new formulations for FMGaBP, which further enhance its computation and communication complexities where the parallel features of FMGaBP are leveraged to multicore architectures.

主权项

1. A method of generating finite element modelling results comprising:
receiving finite element method (FEM) data relating to establishing a FEM problem to be solved for a portion of a physical system being analysed, the FEM data comprising physical dimensions of each element within the portion of the physical system, material data relating the materials forming each element within the portion of the physical system, and physical principles relating to the modelling being performed; generating a FEM mesh comprising at least FEM mesh node locations relating to the portion of the physical system in dependence upon at least the physical dimensions of each element within the portion of the physical system; automatically generating with a microprocessor FEM mesh values for each FEM mesh node location, the FEM mesh value established in dependence upon FEM mesh node location within the portion of the physical system, the material data and physical principles; automatically generating with a microprocessor based upon the FEM mesh node locations a factor graph model, the factor graph model comprising a plurality of random variable nodes and a plurality of factor nodes; and automatically executing a set of belief propagation update rules upon the factor graph model using Gaussian function parameterization and the FEM mesh values, the belief propagation update rules comprising a factor node update rule that a factor node message is sent from each factor node of the plurality of factor nodes to all variable nodes of the plurality of variable nodes to which it is connected and a variable node update rule that a variable node message is sent back from a variable node to each factor node of the plurality of factor nodes to which it is connected; and iteratively executing the belief propagation update rules until a predetermined condition has been met.