Bruce M. Irons

Equation-Solving Algorithms for the Finite-Element Method

Publisher Summary This chapter discusses finite-element solution algorithms with particular reference to programming techniques. It is widely assumed that an algorithm must succeed or fail regardless of the skill, care, and time given to implementing it. The most important choice is the system of housekeeping to be adopted for the various arrays. The algorithm must be considered carefully, because mistakes are expensive to rectify. The diagonal terms decrease monotonically as the reduction proceeds but remain positive. If the final, pivotal value is small compared to the preceding values, then one could have a conditioning problem. The conjugate gradient algorithm is iterative, so that the computing time cannot be accurately forecast. The tests suggest that it does not compete with the frontal Gaussian solution. If, in using the front algorithm, one uses complex examples, one finds that empty spaces appear that are not immediately reoccupied.