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Quadratic element linear elastic boundary elements in Julia

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Bem2d.jl

Bem2d.jl is a Julia library for two-dimensional plane strain linear elastic boundary element (BEM) calculations related to earthquakes and tectonics.

The ideas behind Bem2d.jl are described in detail in the paper: "Bem2d.jl: A quadratic co-location two-dimensional boundary element approach to quasi-static faulting problems with gravity and non-planar topography", Meade, Thompson 2021, Computers & Geoscience

Package Features

  • Analytic quadratic slip and traction elements (Portella et al., 1992)
  • Surface topography & non-planar fault surfaces
  • Unidirectional gravity (Pape and Banerjee, 1987)
  • Kinematically consistent quasi-dynamic earthquake cycles with slip and aging laws

Basic BEM calculation

A simple starting example of a thrust fault with a topographic surface can be generated with:

using Bem2d
include(“examples/faultboxgravitytopo.jl”)

should produce this figure:

thrusttopo

Examples

These serve as reference examples (and some as effectively tests) with the intent of making clear how to build simple to complex BEM models

faultboxgravitytopo.jl - A single planar fault in a box with a non-planar topography and unidirectional gravity. Currently with constant slip elements.

bemvsdeepokada.jl - [works on Linux, because of okada_wrapper dependency] - Comparision between fundamental fullspace 2D elastic disloation soluitons and Okada's half space 3D solutions.

braziltest.jl - Traction only compression of a homogeneous disc (Brazil test)

constvsquadelements.jl - Basic comparision of constant slip vs. 3 node quadratic elements.

discmaterial.jl - A simple two domain problem. An inner annulus surrounded by a an unbounded region with different material properties. Crouch and Starfield solve this for using fictious force vs. the DDM approach here.

gravitybox.jl - Homogenous square compressing under the force of gravity with a no slip bottom boundary condition.

kelvin.jl - Comparison of point source kelvin solution with finite source DDM approximation.

nearsurfaceerror.jl - Comparision of constant element vs. 3 node quadratic element errors when compared with Okada. [works on Linux, because of okada_wrapper dependency]

weldedcircle.jl - A basic two domain example consisting of a circle cut into upper and lower halves with differing material properties. Traction boundary conditions apply on the top of the circle and no-slip boundary conditions on the bottom half.

weldedcirclefault.jl - A basic two domain example consisting of a circle cut into upper and lower halves with differing material properties and fault in the upper domain. The upper half of the circle boundary is traction and no-slip boundary conditions on the bottom half.

Running inside Docker

Bem2d.jl has its own docker image! Before, continuing, follow these directions to make sure you have the latest version of docker and docker-compose:

To test that out, try running docker run hello-world.

If that works, let's launch a Jupyter notebook with Bem2d.jl installed. Run: ./launch_jupyter That should first download or build the docker image which includes installing all the dependencies for Bem2d.jl. Afterwards, it'll launch a Jupyter Lab server instance. Find the line in the output saying [I 19:20:33.891 LabApp] The Jupyter Notebook is running at:. The next line should tell you what port the server is running on. Open your browser to localhost:THATPORT and play around!

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