Fast decomposition of matrices generated by the boundary element method

A new method to reduce the solution time of matrices generated by the Boundary Element Method is presented here. The method involves converting the fully populated system into a banded system by lumping certain coefficients of the matrix into fictitious nodes and then constraining these nodes to accurately represent each coefficient. The major advantages of lumping over the substructuring method are that lumping can be applied to arbitrarily shaped geometries and infinite‐domain problems and that it preserves the diagonal‐dominance of the matrix. It is shown here that the proposed algorithm reduces the rate of increase of solution time t of an n‐degree‐of‐freedom problem from t ∝ n3 to t ∝ n2. Although the algorithm is for thermal problems, its extension to mechanical problems is straightforward. The procedure can easily be incorporated into existing boundary‐element‐based packages.