### Alternative Formulations of The Laplace Transform Boundary Element (LTBE) Numerical Method for the Solution of Diffusion-Type Equations [chapter]

G. J. Moridis
1992 Boundary Element Technology VII
The Laplace Transfbrrn Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs., lt completely elinfinat_ the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solu_,ions are obtained in the Laplace space, and are then inverted numerically to yield the solutic.n in time. The Stehfest and the DeHoog t'orn_'lla.¢,ions of LTBE,
more » ... .¢,ions of LTBE, b_,e.d on two differe,_t i,._versionalgorithms, are investigated. Both formulations produce comparable, extrem_,_y_curate solutions. The Stehfest formulation uses real values for tlm Laplace space parameter A, combines linearly the results of a liufited number of matrix solutions (6 to 8), does not increase comput.er storage, i.ssimple to code, and requires significantly less execution time, but :_ields a solution at a single observation time l for each set of A's. The DeHoog formulation uses complex vMues for the A's, needs more matrix inversions, and uses non-lib.ear combinations of the solutions, but allows solutions _t a range oi' times t.from a single set of ,X's. Compared to the Stehfe_t LTBE, the DeHoog LTBE produces matrices 4 tames as l_ge, increases execution times per matrix inversion by at, least a factor of 12 and the memory requirements by a nfinimum, factor of 4. The Stehf_;:t LTBE seems to have a clear advantage, except in cases involving very steep functiox_sof time. INTROD UCTION In diffusion-type equations, we seek an approximate solution to the PDE 1 aU (x,_,t)