Libmesh sparse matrix pdf

Imagine you have a twodimensional data set with 10 rows and 10 columns such that each element contains a value. In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. Create sparse matrix matlab sparse mathworks italia. Sparse matrices single linear list in rowmajor order. However, if you do not specify the dimension sizes of the output, m and n, then sparse calculates the maxima m maxi and n. By contrast, if most of the elements are nonzero, then the matrix is considered dense. Standard sparse matrix formats results to indirect memory. University of michigan, ann arbor, mi arizona state university, tempe, az. A matrix object used for finite element assembly and numerics. Parallel workflows in computational engineering with. If v is a vector or matrix, then one of the inputs i or j must also be a vector or matrix with the same number of elements any elements in v that are zero are ignored, as are the corresponding subscripts in i and j.

In fact, commercial codes for large lp problems seem to have predated codes for sparse linear equations even though solving a sparse lpproblem requires. However, exposing the class and template structure of lib mesh to users can. An outer product based sparse matrix multiplication accelerator subhankar pal. Compressed sparse column csc, used for efficient and nuanced implementation of core arithmetic operations such as matrix multiplication and addition, as well. Libmeshusers using sparse matrix functions in main. Now imagine, you have a 10 x 10 matrix with only very few elements of the matrix is nonzero.

Useful for storing element stiffness matrices before summation into a global matrix, particularly when you have systems of equations. Sparsematrix access functions for each degree of free dom pair at. Libmesh users using sparse matrix functions in main function from. This class contains pure virtual members that must be overridden in derived. The number of zerovalued elements divided by the total number of elements e. Libmeshusers using sparse matrix functions in main function from. We can also call such data as matrix, in this example it is a dense 10 x 10 matrix. For example, sparse matrices are constructed with one function call per. Implementing sparse matrixvector multiplication on throughputoriented processors nathan bell and michael garland proceedings of supercomputing 09 efficient sparse matrixvector multiplication on cuda nathan bell and michael garland nvidia technical report nvr2008004, december 2008 iterative methods for sparse linear systems yousef saad. This class provides a nice interface to the petsc cbased data structures for parallel, sparse. This class contains pure virtual members that must be overridden in derived classes. The eigensparsematrix class wraps a sparse matrix object from the eigen library. The libmesh library was created to facilitate parallel, adap tive, multiscale. Using a common base class allows for uniform access to sparse matrices from various different solver packages in different formats.