A hybrid finite element‐spectral boundary integral approach: Applications to dynamic rupture modeling in unbounded domains

Abstract

Summary The finite element method (FEM) and the spectral boundary integral method (SBI) have both been widely used in the study of dynamic rupture simulations along a weak interface. In this paper, we present a hybrid method that combines FEM and SBI through the consistent exchange of displacement and traction boundary conditions, thereby benefiting from the flexibility of FEM in handling problems with nonlinearities or small‐scale heterogeneities and from the superior performance and accuracy of SBI. We validate the hybrid method using a benchmark problem from the Southern California Earthquake Center's dynamic rupture simulation validation exercises.We further demonstrate the capability and computational efficiency of the hybrid scheme for resolving off‐fault heterogeneities by studying a 2D in‐plane shear crack in two different settings: one where the crack is embedded in a high‐velocity zone and another where it is embedded in a low‐velocity zone. Finally, we discuss the potential of the hybrid method for addressing a wide range of problems in geophysics and engineering.

A Novel Hybrid Finite Element-Spectral Boundary Integral Scheme for Modeling Earthquake Cycles: Application to Rate and State Faults with Low-Velocity Zones

“…This account for further computational savings. The truncation of the domain in the hybrid scheme accounts for savings in the overall run time, as well as memory utilization, as demonstrated in earlier studies (Ma et al, 2018). It is noted that the correction steps involved in the proposed algorithm incur additional computation cost; however, the cost is far less than the cost associated with modeling the entire domain.…”

“…The hybrid formulation considered here is a combination of the finite element method (FEM) and the spectral boundary integral (SBI) method previously introduced by (Ma et al, 2018).…”

“…This framework proved to yield accurate results, at a fraction of the computational cost of a purely domain-based scheme. While initially developed to study the elastodynamics of an anti-plane problem, Ma et al extended the hybrid method formulation to a 2-D in-plane setting and replaced the finite difference in the bulk with a finite element formulation (Ma et al, 2018), enabling more flexibility in handling complex boundaries and fault zone topologies (Ma & Elbanna, 2019).…”

A Novel Hybrid Finite Element‐Spectral Boundary Integral Scheme for Modeling Earthquake Cycles: Application to Rate and State Faults With Low‐Velocity Zones

“…This account for further computational savings. The truncation of the domain in the hybrid scheme accounts for savings in the overall run time, as well as memory utilization, as demonstrated in earlier studies (Ma et al, ). It is noted that the correction steps involved in the proposed algorithm incur additional computation cost; however, the cost is far less than the cost associated with modeling the entire domain.…”

Machine learning for composite materials

“…It is this reason that many studies in the literature have focused on advancing computational tools and methods to model various types of materials. [10][11][12][13][14][15][16][17][18] Compared with solely predicting properties of known materials, designing new materials to achieve tunable properties is a more important problem for scientific and engineering purposes. In fact, predicting materials' properties and designing materials are quite different problems, in which the former is often referred to as a forward modeling problem and the latter is an inverse design problem.…”