High-performance direct solution of finite element problems on multi-core processors

A direct solution procedure is proposed and developed which exploits the parallelism that exists in current symmetric multiprocessing (SMP) multi-core processors. Several algorithms are proposed and developed to improve the performance of the direct solution of FE problems. A high-performance sparse direct solver is developed which allows experimentation with the newly developed and existing algorithms. The performance of the algorithms is investigated using a large set of FE problems. Furthermore, operation count estimations are developed to further assess various algorithms. An out-of-core version of the solver is developed to reduce the memory requirements for the solution. I/O is performed asynchronously without blocking the thread that makes the I/O request. Asynchronous I/O allows overlapping factorization and triangular solution computations with I/O. The performance of the developed solver is demonstrated on a large number of test problems. A problem with nearly 10 million degree of freedoms is solved on a low price desktop computer using the out-of-core version of the direct solver. Furthermore, the developed solver usually outperforms a commonly used shared memory solver.Ph.D.Committee Chair: Will, Kenneth; Committee Member: Emkin, Leroy; Committee Member: Kurc, Ozgur; Committee Member: Vuduc, Richard; Committee Member: White, Donal

ParallelLCA : a foreground aware parallel calculator for life cycle assessment

Life Cycle Assessment (LCA), which aims to assess the environmental impacts during the life cycle of a system product (S) (e.g., production of aluminum in Quebec), can be used to compare different systems built with different types of materials to determine which is the least harmful to the environment. The calculation in LCA represents a computational challenge as it is dependent on the size of the system, the number of iterations in the Monte-Carlo simulation, and the number of uncertain variables in the system. First, the solving of a linear system of dimensions in the order of 10,000 equations by 10,000 unknown variables is required for the base case. Second, the building of a graph iterative in nature with minimum dimensions of 10,000 vertices. Third, the computing of a Monte-Carlo simulation requiring several thousands of iterations to converge is to be computed. Finally, a sensitivity analysis which requires the computing of millions of correlations between vectors each having a dimension that is proportional to the number of iterations in the Monte-Carlo simulation. To best solve the computational challenges present in LCA, this research benefits from well established libraries that solve large sparse linear systems and performs large sparse matrix computing. Also, this thesis adopted mathematical optimizations that removed the matrix inverse step from the contribution analysis module, which is very expensive, as well as other algorithmic optimizations that removed the large and variant part of the LCA supply-chain from the matrix component of the various calculation phases. Furthermore, this research experimented with libraries such as OpenMP, MPI, and Apache Spark to parallelize the computation. First, the thesis will discuss the literature regarding these computational opportunities. Second, it will present a proposed LCA calculator for implementing an efficient LCA computation. Finally, it will present the performance of computing the different phases of LCA for various dimensions of the system (S) and concludes with suggestions for improvement and future development