Journal of Advanced Applied Scientific Research -ISSN: 2454-3225 M.Kamalian et.al JOAASR-Vol-1-10-May-2017 A fast BIEM algorithm to evaluate seismic ground response in 2D Elastic Time Domain M.Kamalian 1* , M.Saffar 2, 1* Professor, Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES) 2 Ph.D. Candidate, Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES) * Corresponding author Email: kamalian@iiees.ac.ir Abstract Since the topography and surface irregularities of the terrain have a significant effect on the seismic response of the earth's surface, the numerical analysis using boundary element method in elastodynamics, which leads to a significant increase in the number of degree of freedom and stiffness matrix dimension, as well as the sparse and unsymmetrical structure of stiffness matrix, indicates the inefficiency of the conventional method. This paper presents a fast boundary element algorithm in seismic analysis of two-dimensional elastic media for the first time. In the proposed method, instead of the usual node-to-node, a method of cell-to-cell relation method is implemented by hierarchy tree structure. In addition, the Plane Wave Time Domain algorithm and the Iterative method has been used to solve a system of equations which increases the speed of network convergence, especially in high degrees of freedom that has not been used in the study of the seismic waves’ response yet. Nowadays, this new algorithm adopts for investigating the response wave fields of electrical, magnet [1], acoustic and thermal conductivity which are discussed in details in various articles and books. Keywords: Plane Wave Time Domain (PWTD), Fast Boundary Element, Iterative Solver, Hierarchy tree, Degree of Freedom (DOF) Introduction: As the need to implement large-scale surface topographies, efficient algorithm for evaluation of seismic ground response becomes indispensable. For analyzing the transient wave in elasto-dynamic media, most enhanced numerical methods are based on either integral or differential equations. Differential equation methods, such as Finite- Difference and Finite-Element, are more capable to model finite and inhomogeneous media, while integral equation methods represent two notable advantages in analyzing surface materials’ behavior: 1) Integral equation methods such as boundary element only need to mesh exterior (boundary) surface, while differential equation methods are based on body (volumetric) discretization, which aggressively increases DOF compared to integral equation methods. 2) Green functions in shape of main elements of integral equations implicitly impose radiation condition, which eliminates the need for local absorbing boundary conditions.