Patent ID: 8428923

Claim:
A non-transitory program storage device readable by a machine tangibly embodying a program of instructions executable by the machine to perform a method comprising: simulating a hydraulic fracture in an Earth formation, the formation including a multilayered reservoir, wherein a mesh overlays the hydraulic fracture thereby defining a plurality of fracture elements; and calculating and determining an influence coefficient matrix having spatially related indices, wherein the spatially related indices relate influence coefficient matrix elements to corresponding fracture elements using a computing device including a program storage device readable by the computing device tangibly embodying a program of instructions executable by the computing device, and wherein the calculating and determining an influence coefficient matrix having spatially related indices comprises: determining spectral coefficients corresponding to each layer of the multilayered reservoir, wherein the spectral coefficients do not include a time dependency; performing an exponential approximation to determine exponential expansion coefficients; and assembling the influence coefficient matrix according to the exponential expansion coefficients.