scholarly journals MPI-OpenMP hybrid simulations using boundary integral equation and finite difference methods for earthquake dynamics and wave propagation: Application to the 2007 Niigata Chuetsu-Oki earthquake (Mw6.6)

2011 ◽  
Vol 4 ◽  
pp. 1496-1505 ◽  
Author(s):  
Hideo Aochi ◽  
Fabrice Dupros
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Boundary Integral Equation ◽  
Finite Difference Methods ◽  
Boundary Integral ◽  
Earthquake Dynamics ◽  
Difference Methods ◽  
Hybrid Simulations

Hybrid modeling of elastic‐wave propagation in two‐dimensional laterally inhomogeneous media

Geophysics ◽  
1987 ◽  
Vol 52 (6) ◽  
pp. 765-771 ◽  
Author(s):  
B. Kummer ◽  
A. Behle ◽  
F. Dorau
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Hybrid Scheme ◽  
Finite Difference Techniques

We have constructed a hybrid scheme for elastic‐wave propagation in two‐dimensional laterally inhomogeneous media. The algorithm is based on a combination of finite‐difference techniques and the boundary integral equation method. It involves a dedicated application of each of the two methods to specific domains of the model structure; finite‐difference techniques are applied to calculate a set of boundary values (wave field and stress field) in the vicinity of the heterogeneous domain. The continuation of the near‐field response is then calculated by means of the boundary integral equation method. In a numerical example, the hybrid method has been applied to calculate a plane‐wave response for an elastic lens embedded in a homogeneous environment. The example shows that the hybrid scheme enables more efficient modeling, with the same accuracy, than with pure finite‐difference calculations.

Numerical Study on the Growth and Collapse of a Cavitation Bubble inside a Rigid Cylinder with a Compliant Coating

2014 ◽  
Vol 875-877 ◽  
pp. 1194-1198
Author(s):  
Fardin Rouzbahani ◽  
M.T. Shervani-Tabar
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Cavitation Bubble ◽  
Numerical Study ◽  
Finite Difference Methods ◽  
Life Time ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Compliant Coating ◽  
Rigid Cylinder

In this paper, growth and collapse of a cavitation bubble inside a rigid cylinder with a compliant coating (a model of humans vessels) is studied using Boundary Integral Equation and Finite Difference Methods. The fluid flow is treated as a potential flow and Boundary Integral Equation Method is used to solve Laplaces equation for velocity potential. The compliant coating is modeled as a membrane with a spring foundation. The effects of the parameters describing the flow and the parameters describing the compliant coating on the interaction between the fluid and the cylindrical compliant coating are shown throughout the numerical results. It is shown that by increasing the compliancy of the coating, the bubble life time is decreased and the mass per unit area has an important role in bubble behavior.

Modeling of Wave Propagation in the Unsaturated Soils Using Boundary Element Method

2017 ◽  
Vol 743 ◽  
pp. 158-161
Author(s):  
Andrey Petrov ◽  
Sergey Aizikovich ◽  
Leonid A. Igumnov
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Equations ◽  
Boundary Integral Equation ◽  
Boundary Integral Equations ◽  
Water Pressure ◽  
Boundary Integral ◽  
Element Method

Problems of wave propagation in poroelastic bodies and media are considered. The behavior of the poroelastic medium is described by Biot theory for partially saturated material. Mathematical model is written in term of five basic functions – elastic skeleton displacements, pore water pressure and pore air pressure. Boundary element method (BEM) is used with step method of numerical inversion of Laplace transform to obtain the solution. Research is based on direct boundary integral equation of three-dimensional isotropic linear theory of poroelasticity. Green’s matrices and, based on it, boundary integral equations are written for basic differential equations in partial derivatives. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. To approximate the boundary consider its decomposition to a set of quadrangular and triangular 8-node biquadratic elements, where triangular elements are treated as singular quadrangular. Every element is mapped to a reference one. Interpolation nodes for boundary unknowns are a subset of geometrical boundary-element grid nodes. Local approximation follows the Goldshteyn’s generalized displacement-stress matched model: generalized boundary displacements are approximated by bilinear elements whereas generalized tractions are approximated by constant. Integrals in discretized boundary integral equations are calculated using Gaussian quadrature in combination with singularity decreasing and eliminating algorithms.

FINITE DIFFERENCE METHODS FOR ELASTIC WAVE PROPAGATION IN LAYERED MEDIA

2004 ◽  
Vol 12 (02) ◽  
pp. 257-276 ◽  
Author(s):  
M. TADI
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Finite Difference Methods ◽  
Layered Media ◽  
Approximate Model ◽  
Elastic Wave Propagation ◽  
Elastic Solids ◽  
Long Time ◽  
Difference Methods

This paper is concerned with the numerical modeling of elastic wave propagation in layered media. It considers two isotropic homogeneous elastic solids in perfect contact. The interface is parallel to the free surface. Two finite difference methods are developed. The usefulness of the methods are investigated for long time simulations and the accuracy of the results are compared with the response from an approximate model.

Modeling of low‐frequency Stoneley‐wave propagation in an irregular borehole

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1047-1058 ◽  
Author(s):  
Kazuhiko Tezuka ◽  
C. H. (Arthur) Cheng ◽  
X. M. Tang
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Methods ◽  
Low Frequency ◽  
Field Application ◽  
Boundary Integral ◽  
Modeling Method ◽  
Stoneley Wave ◽  
Wave Interactions ◽  
Property Changes

A fast modeling method is formulated for low‐frequency Stoneley‐wave propagation in an irregular borehole. This fast modeling method provides synthetic waveforms which include the effects of two borehole irregularities, diameter changes (washout), and formation property changes. The essential physics of the low‐frequency Stoneley waves are captured with a simple 1-D model. A mass‐balance boundary condition and a propagator matrix are used to express Stoneley‐wave interactions with the borehole irregularities. The accuracy of the proposed method was confirmed through comparison with existing finite‐difference and boundary integral modeling methods that yielded cross‐correlations greater than 0.98. Comparison of synthetic records calculated for an actual borehole with field records showed qualitative agreement in the major reflections because of the washout zones, but showed some disagreements in the reflections caused by the fractures. Since the synthetic records include only information relating to the borehole geometry and the elastic properties of formation, the reflection caused by the fracture will appear only in the field record. These results suggest the possibility of distinguishing Stoneley‐wave reflections caused by fractures from those caused by borehole irregularities. Further, the fast computational speed of this method—over 300 times faster than either boundary integral or finite‐difference methods—makes it quite suitable for field application.

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