Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Materials Hohai University Nanjing 211100 China;
Department of Mechanical and Mechatronic Engineering National Taiwan Ocean University Keelung 202-24 Taiwan;
Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and Materials Hohai University Nanjing 211100 China;
School of Electromechanic Engineering Qingdao University Qingdao 266071 China;
Institute of Applied Mathematics Shandong University of Technology Zibo 255049 China;
Poisson equation; multiple/scale/direction Trefftz method; multiple-scale polynomial method; irregular domain; inverse Cauchy problem;