This project implements different parallel message-passing approaches for Matrix LU Factorisation. The goal is to compare the execution time for different agglomeration schemes and the cost of partial pivoting. We based our work on Michael T. Heath's class Parallel Numerical Algorithms

We implemented 3 agglomeration schemes and a sequential version:

• Agglomeration by adjacent lines
• Agglomeration by cyclic lines
• Agglomeration by 2D adjacent blocks

For the all versions except the 2D blocks, it is possible to specify if you want to use partial pivoting. The default behavior of the applications is to generate a random square matrix and calculate the factorization. The program does not check if a factorization actually exists. The result is stocked in the same matrix, the lower-triangular matrix containing the L matrix and the main diagonal and upper triangular matrix containing the U matrix.

Usage

Arguments:

• -m : Required. Size of the matrix. For the moment the applications only treat square matrixes, so only one size is required.
• -f : Text file to specify the input matrix. If not specified the application will generate a random matrix.
• -s : Solution file, to verify the result calculated by the application.
• -i: print the result to screen.
• -w : write the result to file.
• -p: use partial pivoting. Not available for lu_mpi_cart
• -x, y : Required for lu_mpi_cart, specify the size of a block, the sizes must be divisors of the number of nodes used and must

The makefile contains basic tests and a command to compare times for all applications given a size of a matrix and a number of nodes to use.

This work was done for INF7235 at UQAM. Our original report was written in French and is available in the latex folder.