Commit 58a64e33 authored by Jan Zapletal's avatar Jan Zapletal

MAINT: renamed manual dir to fig

parent 3e0b9484
......@@ -10,61 +10,61 @@ The purpose of the library is to generate the Dirichlet-to-Neumann (Steklov-Poin
In total (all-floating) BETI we consider a Neumann boundary value problem for the Laplace equation in 3D for every subdomain,
<img src="manual/bvp.png" alt="BVP"> with the compatibility condition <img src="manual/compat.png" alt="compatibility condition">.
<img src="fig/bvp.png" alt="BVP"> with the compatibility condition <img src="fig/compat.png" alt="compatibility condition">.
The domain is decomposed into a set of plane triangles
<img src="manual/omega.png" alt="Omega"/>.
<img src="fig/omega.png" alt="Omega"/>.
The heatDtN library provides a Dirichlet-to-Neumann operator
<img src="manual/sp.png" alt="Steklov-Poincaré"/>
<img src="fig/sp.png" alt="Steklov-Poincaré"/>
discretized via the Galerkin boundary element method as
<img src="manual/sph.png" alt="Steklov-Poincaré"/>
<img src="fig/sph.png" alt="Steklov-Poincaré"/>
or in its non-symmetric form as
<img src="manual/sphn.png" alt="Steklov-Poincaré"/>.
<img src="fig/sphn.png" alt="Steklov-Poincaré"/>.
The individual matrices composing the operator are given as
<img src="manual/vh.png" alt="Vh"/>,
<img src="fig/vh.png" alt="Vh"/>,
<img src="manual/kh.png" alt="Kh"/>,
<img src="fig/kh.png" alt="Kh"/>,
<img src="manual/dh.png" alt="Dh"/>,
<img src="fig/dh.png" alt="Dh"/>,
<img src="manual/mh.png" alt="Mh"/>
<img src="fig/mh.png" alt="Mh"/>
with the globally continuous piecewise linear functions <img src="manual/phi.png" alt="phi"/>. The globally continuous piecewise linear approximation of the Dirichlet boundary data satisfying
with the globally continuous piecewise linear functions <img src="fig/phi.png" alt="phi"/>. The globally continuous piecewise linear approximation of the Dirichlet boundary data satisfying
<img src="manual/scaling.png" alt="scaling condition"/>
<img src="fig/scaling.png" alt="scaling condition"/>
can be obtained from the discretized boundary integral equation
<img src="manual/bem.png" alt="BEM"/>
<img src="fig/bem.png" alt="BEM"/>
with the Neumann data discretized by piecewise constant functions and
<img src="manual/beta.png" alt="beta"/>,
<img src="fig/beta.png" alt="beta"/>,
<img src="manual/ai.png" alt="ai"/>, <img src="manual/a.png" alt="a"/>.
<img src="fig/ai.png" alt="ai"/>, <img src="fig/a.png" alt="a"/>.
### Volume evaluation
By solving the global BETI problem we obtain the Dirichlet data. In order to evaluate the solution in every subdomain we solve the auxiliary Dirichlet problem
<img src="manual/bvpd.png" alt="BVP">
<img src="fig/bvpd.png" alt="BVP">
by the boundary integral equation
<img src="manual/dirbie.png" alt="BIE">
<img src="fig/dirbie.png" alt="BIE">
and use the representation formula
<img src="manual/repr.png" alt="representation formula">.
<img src="fig/repr.png" alt="representation formula">.
## Compilation
......@@ -190,7 +190,7 @@ To include the heatDtN module include the parameter `HEATDTN::PATH = /path/to/he
### Configuration
In an ECF file, set `DISCRETIZATION` to `BEM`. An example of a configuration file can be found [here](manual/heatdtn.ecf).
In an ECF file, set `DISCRETIZATION` to `BEM`. An example of a configuration file can be found [here](fig/heatdtn.ecf).
## References
......
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