Element-by-element solution procedures for nonlinear transient heat conduction analysis

The development of algorithms was undertaken whose resource needs grow only linearly with problem size. In addition, these new algorithms will fully exploit the parallel processing capability available in the new generation of multiprocessor computers. The approach taken in the element by element solution procedures is to approximate the global implicit operator by a product of lower order operators. This type of product approximation originated with ADI techniques and was further refined into the method of fractional steps. The current effort involves the use of a more natural operator split for finite element analysis based on element operators. This choice of operator splitting based on element operators has several advantages. First, it fits easily within the architecture of current FE programs. Second, it allows the development of parallel algorithms. Finally, the computational expense varies only linearly with the number of elements. The particular problems considered arise from nonlinear transient heat conduction.