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An implementation of a locally modified finite element method for interface problems in deal.II

Stefan Frei; Thomas Richter; Thomas Wick


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    <subfield code="a">&lt;p&gt;This source code contains an implementation of the locally modified finite element method first proposed&amp;nbsp; by S. Frei, T. Richter, SIAM Journal on Numerical Analysis 52 (5), 2315-2334. This method is a simple approach to solve interface problems, as arising in fluid-structure-interactions or multi-phase flows, or problems on complex boundaries.&lt;/p&gt;

&lt;p&gt;The implementation is contained in the files locmodfe.cc/h, together with a user program (step-modfe.cc) that is similar to many deal.II steps (&lt;a href="http://www.dealii.org"&gt;www.dealii.org&lt;/a&gt;) and a problem-specific file (problem.h) with specific data for some numerical tests provided in the src folder. The source code is based on the deal.II.8.5.0 version.&lt;br&gt;
&amp;nbsp;&lt;/p&gt;

&lt;p&gt;In the test folder, we provide the parameter files parameters_test_case_1/2.prm, where algorithmic, numerical and physical parameters can be changed. In the current version, parameters are pre-set for the two numerical tests. For the meaning of the parameters, see the detailed comments in the parameter files.&lt;br&gt;
&amp;nbsp;&lt;br&gt;
Moreover, we provide the output that the program writes to a terminal in the files test_case_1/2.dlog in the same folder, for a comparison of the terminal output results.&lt;/p&gt;

&lt;p&gt;In the build folder, the file CMakeLists.txt can be used to create a Makefile using cmake, see the explanations given in README.txt. Moreover, the README.txt file provides detailed installation instructions and a compact overview of all source files.&lt;/p&gt;

&lt;p&gt;Algorithmic descriptions and details of the delivered source code are provided in S. Frei, T. Richter, T. Wick; 2018, arXiv preprint &lt;a href="https://arxiv.org/abs/1806.00999"&gt;arXiv:1806.00999&lt;/a&gt;&lt;/p&gt;

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