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Assembly and linear algebra operations on distributed matrices and vectors such as sparse matrix-vector multiplication, however, requires MPI 1 1 1 via Message Passing Interface Message Passing Interface Forum, communication between ranks which is minimized using efficient mesh partitioning and renumbering of nodes. Unstructured mesh based codes, such as those based on the finite element method, allow for flexibility in distribution of material properties and geometry that is difficult to accommodate in analytical or semi-analytical codes. An example input file containing a hollow pressurized magma chamber beneath the Okmok volcano with is available here. These input files were automagically generated using the exo2inp utility, and accompanying Exodus II files i. Some of the files below may or may not be up-to-date.

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Quasi-static influx of magma through a conduit followed by fault slip use a sparse direct solver ex4. In this article, we present Defmod, an open source, fully unstructured, two or three dimensional, parallel finite element code for modeling crustal deformation over time defmos ranging from milliseconds to thousands of years.

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Deformation due to withdrawal of groundwater from basin ex9 a. Once again, we find good agreement between the two solutions. The video above shows coseismic deformation, visualized using a wrapped color scale, due to slip on a reverse fault. Figure S 1 shows some results cefmod using Defmod.

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The constraints are implemented using Lagrange Multipliers, which results in the system of equations: Unlike Abaqus, Defmod uses stabilized linear elements and therefore can solve for the pressure defmodd more efficiently.

Use the demfod instructions to download and run: This results in a coupled system of equations, of the form: The author was partially supported by U. By using stabilized linear elements, Defmod can solve poroelasticity problems more efficiently than codes that use quadratic approximation for displacements and linear for pressure. A permeability of 1. We calculate surface displacements at a distance of 25 km from the source. Use the following instructions to create the above input file s: Unstructured mesh based codes, such as those based on the finite element method, defmoc for flexibility in distribution of material properties and geometry that is difficult to accommodate in analytical or semi-analytical codes.

In the current version of the code, prescribed loading is supported.

To circumvent the Ladyzenskaja-Babuska-Brezzi restrictions on linear elements, Defmod uses the local pressure projection scheme proposed by Bochev and Dohrmann For example, Figure 1 shows the pressure field inside a two dimensional poroelastic domain, discretized using linear triangular elements, following co-seismic slip on a thrust fault, with and without stabilization.

The mass matrix M is assumed to be lumped, therefore is diagonal, and easy to invert. Figure 8 shows the Defmod solution along with the Abaqus solution, along a vertical cross-section, at 1.

Benchmarking Defmod, an open source FEM code for modeling episodic fault rupture

Figure 6 shows a snapshot of the wave field calculated using Defmod at the t h time step. The constraints are implemented using Lagrange Multipliers, which results in the system of equations:. Quasi-static fault slip ex3. Xefmod Abaqus, Defmod uses full integration for the elastodynamic problem.

Assembly defmmod linear algebra operations on distributed matrices and vectors such as sparse matrix-vector multiplication, however, requires MPI 1 1 1 via Message Passing Interface Message Passing Interface Forum, communication between ranks which is minimized using efficient mesh partitioning and renumbering of nodes.

The time-dependent system of equations is solved using an incremental loading scheme Smith and Griffiths, All element level calculations, e.

Some results obtained using Defmod are available here. Elastodynamic fault slip ex6. Because the number of iterations in the iterative solver for quasistatic problems can slightly vary with the dwfmod of processor cores, we fix the number of iterations. Results for both, defmood elastodynamic and implicit quasistatic problems are shown in Table 1. The reason for choosing such a simple problem is because it includes calculations that are common to all types of problems, irrespective of rheology i.

The vertical and horizontal displacements, calculated over time, using Defmod and Abaqus, are in good agreement with each other, as shown in Figure 6. Using sefmod finite element method, the equation can be written in the semi discrete form as: