The Displacement Discontinuity Method (DDM) is one of the most popular numerical methods in simulating hydraulic fracturing problems. Despite its superior advantages in solving fracture modeling problems, this method becomes computationally expensive when the number of degrees of freedom (DOF) increases. An example takes place in the study of two-dimensional fracturing problems with multiple fractures propagating from one or more wells. It would also occur in three-dimensional problems where typically the number of elements exceeds a few thousands. Additionally, including poroelasticity into the problem makes this method even more computationally expensive because of the necessity to build a time-marching procedure. The Fast Multipole Method (FMM) is a computational method to efficiently compute matrix-vector products with a controllable error. Unlike the conventional Boundary Element Method (BEM), in FMM the interaction between far-field sources and influenced points are calculated by initially concentrating a cluster of far-field sources into a separate point, then the effect of these concentrated forces on each influenced point is calculated.
A Novel Approach to Efficiently Solve Displacement Discontinuity Problems in Poroelastic Media
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Rezaei, A. , Siddiqui, F. , Bornia, G. , Soliman, M. Y., Rafiee, M. , and S. Morse. "A Novel Approach to Efficiently Solve Displacement Discontinuity Problems in Poroelastic Media." Paper presented at the 51st U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, California, USA, June 2017.
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