Direct Linear Equation Solver

The direct sparse solver uses a “multifront” technique that can reduce the computational time to solve the equations dramatically if the equation system has a sparse structure. Such a matrix structure typically arises when the physical model is made from several parts or branches that are connected together; a spoked wheel is a good example of a structure that has a sparse stiffness matrix. Space frames and other structures modeled with beams, trusses, and shells often have sparse stiffness matrices. In contrast, a blocky structure—such as a single, solid, three-dimensional block (see Elastic-plastic line spring modeling of a finite length cylinder with a part-through axial flaw)—provides little opportunity for the sparse solver to reduce the computer time. For large blocky structures, the iterative linear equation solver may be more efficient (see Iterative Linear Equation Solver).