Based on the merits of direct Trefftz method and singular boundary element method (BEM), a modified direct Trefftz method is suggested to capture the boundary solutions as well as the domain solutions at the same time. Compared to the classical direct Trefftz method, the modified direct Trefftz method can calculate the response inside the domain and still have the properties of high accuracy. Compared to the singular BEM, the modified direct Trefftz method avoids the singularity of fundamental solutions and its corresponding Cauchy Principal Value integral evaluation, and thus can archive much higher accuracy in solutions compared to the singular BEM method. And the modified direct Trefftz method unites the boundary value evaluation as well as the domain value evaluation into one coefficient matrix and solve them in one step, unlike the classical direct Trefftz method, indirect Trefftz method and the singular BEM, which solve the problem in two stages, ¾ get the boundary values first, ¾ solve the inside domain values next. So the proposed modified direct Trefftz method has the same accuracy as the classical direct Trefftz method, but it simplifies the programming procedures, input preparation, and saves the CPU time up to 60%. In order to show the higher accuracy of the modified Trefftz method, three two-dimensional potential problems are used to validate the model and compared with the singular BEM. And the sensitivity of mesh density, the effect of the number of Trefftz functions and high condition number inherent with the Trefftz method are discussed. The results also show that the high condition number can be reduced by a couple of programming techniques either using the domain geometry transformation or using particular solvers for those special matrixes.

modified direct Trefftz method, singular BEM, sensitivity analysis.