QUASI-LINEAR BOUNDARY-ELEMENT METHOD FOR NONLINEAR POISSON TYPE PROBLEMS

A novel boundary element procedure called the quasilinear boundary element method (QBEM) is developed to solve two dimensional non-linear Poisson type problems, The forcing function of the Poisson type equation is linearized and the resulting terms are transferred to the boundary using a fourth order transformation. This results in boundary only discretization and thus retains all the advantages of the BEM for linear problems. The method provides extremely accurate results for mildly non-linear forcing functions. For strongly non-linear forcing functions, the method is used at a subdomain level and produces good results with only a few subdomains. The method is illustrated by a few test cases and the results compare favorably with solutions obtained through known methods such as the dual reciprocity method (DRM).