Commit c84db336 authored by Jan Zapletal's avatar Jan Zapletal

ENH: updated readme

parent 7f75f0f7
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## About the program
The purpose of the library is to generate the Dirichlet-to-Neumann (Steklov-Poincaré) operator for the Laplace equation in 3D. The operator can be used to solve the stationary heat equation or an electrostatic problem and is primarily designed to be used in a boundary element tearing and interconnecting (BETI) solver. The operator is discretized by the Galerkin boundary element method.
The purpose of the library is to generate the Dirichlet-to-Neumann (Steklov-Poincaré) operator for the Laplace equation in 3D. The operator can be used to solve the stationary heat equation or an electrostatic problem and is primarily designed to be used in a boundary element tearing and interconnecting (BETI) solver [1,2]. The operator is discretized by the Galerkin boundary element method.
## Mathematical background
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* `nElems` ... number of triangular elements
* `elems` ... indices to the array of nodes defining triangular elements `{ i1, j1, k1, i2, j2, k2, ... }`, exterior normal direction to *i*-th element **must** agree with ((xj,yj,zj)-(xi,yi,zi))x((xk,yk,zk)-(xj,yj,zj)),
* `alpha` ... heat conduction parameter,
* `qType` ... `0` for semi-analytic quadrature, `1` for regularized numerical scheme,
* `qType` ... `0` for semi-analytic quadrature [3-5], `1` for regularized numerical scheme [6-7],
* `orderNear` ... near-field quadrature order, choose from {1,...,7} for `qType = 0` (`5` recommended), {3,...,10} for `qType = 1` (`4` recommended),
* `orderFar` ... far-field quadrature order, choose from {0,...,7}, (`4` recommended, `0` uses near-field quadrature for far-field as well),
* `data` ... pointer to heatDtN data,
......@@ -192,6 +192,31 @@ To include the heatDtN module include the parameter `HEATDTN::PATH = /path/to/he
In an ECF file, set `DISCRETIZATION` to `BEM`. An example of a configuration file can be found [here](manual/heatdtn.ecf).
## References
[1] O. Steinbach, Numerical Approximation Methods for Elliptic Boundary Value Problems:
Finite and Boundary Elements, Texts in applied mathematics, Springer, 2008.
[2] G. Of, O. Steinbach, The all-floating boundary element tearing and interconnecting method,
Journal of Numerical Mathematics 17 (4) (2009) 277–298.
[3] O. Steinbach, Galerkin– und Kollokations–Diskretisierungen für Randintegralgleichungen in
3D —Dokumentation—, internal report (2004).
[4] J. Zapletal, J. Bouchala, Effective semi-analytic integration for hypersingular Galerkin
boundary integral equations for the Helmholtz equation in 3D, Appl. Math. 59 (5) (2014)
527–542. https://doi.org/10.1007/s10492-014-0070-6.
[5] J. Zapletal, G. Of, Merta, M. Parallel and vectorized implementation of analytic
evaluation of boundary integral operators, Engineering Analysis with Boundary Elements
96 (2018) 194-208. https://doi.org/10.1016/j.enganabound.2018.08.015
[6] S. Erichsen, S. A. Sauter, Efficient automatic quadrature in 3-d Galerkin BEM, Computer
Methods in Applied Mechanics and Engineering 157 (3–4) (1998) 215–224. https://doi.org/10.1016/S0045-7825(97)00236-3.
[7] S. A. Sauter, C. Schwab, Boundary Element Methods, Springer Series in Computational
Mathematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011. https://doi.org/10.1007/978-3-540-68093-2_4.
## Licence
Copyright (c) 2018, IT4Innovations National Supercomputing Centre, Ostrava, Czech Republic
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