A focus of my current research is to develop numerical methods for the accurate simulation of sound and seismic waves. This waves usually occur in very large domains. For the computational purpose, the original unbounded wave problems need to be transformed into bounded ones. To accomplish this goal artificial boundaries are chosen to truncate the infinite domains. The challenge is to define absorbing boundary conditions (ABC) on these artificial boundaries such that the solutions of the new bounded problems approximate to a reasonable degree the solutions of the original unbounded problems in their common domains. In part, my efforts and those of my students and collaborators have been in deriving computational advantageous ABC and the formulation of a high order and high accurate numerical methods inside the truncated domain.
In this talk, I will describe in some details our work. Also, I will include numerical results which demonstrate the improved accuracy and simplicity of our formulation when compared with commonly used ABC.
Dr. Vianey Villamizar has been a professor of Mathematics at Brigham Young University (BYU) since 2000. After receiving his BS and MS in Mathematics at Universidad Central de Venezuela (UCV), he earned a Ph.D. in Applied Mathematics at Rensselaer Polytechnic Institute (RPI) under the direction of Dr. Julian D. Cole. Then, he was in a postdoctoral position at Northwestern University (NU) for two years. After his post-doc, he returned as a faculty to the UCV for thirteen years before becoming a faculty at BYU. His areas of research are Acoustic, Electromagnetic, and Elastic Wave Propagation, Grid Generation, Numerical Solutions of PDE, Asymptotic Methods.