DIRECTFN package is free software for the accurate and efficient evaluation of 4-D singular integrals arising from Galerkin MoM surface integral equation formulations over conforming triangular or quadrilateral meshes. The fully-numerical algorithms of DIRECTFN are suitable for the following applications:

• Weakly and strongly singular kernels
• Planar and curvilinear elements
• Basis/testing functions of arbitrary order
• Problem-specific Green's functions (e.g. expressed in spectral integral form)
• From zero frequency to frequencies beyond microwaves
• Spectral convergence to machine precision

The complete manual for the use of the library can be found in ReadMe.pdf.

The source code of DIRECTFN is written in C++11. Also, mex plugins are available to provide a fast Matlab interface to this functionality. You are welcome to report any bugs found while testing!

This repository is organized as follows:

• ./include folder contains headers of the library with declarations only.
• ./src folder contains source files where all the templates are instantiated in corresponding files properly. So, in the client programs, one can use the templated classes which have been precompiled already.
• ./lib is the target path to store the compiled static library, which can be further used, e.g. in Matlab interface, or Python wrappers.
• ./tests directory contains some initial examples how to use the library in your own code.
• ./examples folder contains the scripts to reproduce the results, presented in paper [2].

The provided static library and examples can be compiled using make utility. Therefore, it requires Windows users to have some Linux-like environment, such as Cygwin, or MinGW and MSYS2. However, the other possible option is to use nmake utility from Visual Studio (see Compilation with nmake).

The following steps are necessary for compilation:

• If you use MSYS2, launch the MSYS2 console, and add to the path your compiler environment. If you are using Octave, you must use the same compiler that you will use to generate the Mex files in Octave. In this case, add to the path the Octave-provided version of GCC, e.g. "\Octave-4.4.0\bin" where is your Octave installation path, and assuming Octave version 4.4.0.

• Go to the ./settings directory and create or copy-modify platform-specific Makefile.your_cpu_alias. Here the your_cpu_alias is an alias for your system compiler (like intel, gcc620, clang or so). This alias is just an abbreviation to distinguish different Makefiles and can be any name you like.

• Define environment variable CPU=your_cpu_alias. It can be done by the command

 export CPU=your_cpu_alias

or by figuring out the CPU explicitly when compiling the code with make utility:

 make CPU=your_cpu_alias

• Next, add the following lines to the end of Makefile.in:

ifeq ($(CPU),your_cpu_alias)
    include $(MF_PREFIX)/Makefile.target
endif

• Finally, go to the ./lib/unix folder and type

 make

or

 make CPU=your_cpu_alias

This command will compile the code and move the static library into the ./lib folder. Default name for the library is directfn (thus, it will be compiled and built in the static library file libdirectfn.a). You can change the name in ./settings/Makefile.in by defining DIRECTFN_LIB_NAME variable.

In order to enable working with the nmake utility, we provide also special makefiles for it, since the syntax is slightly different from the one that make uses. To compile the source code with nmake you should do the following simple steps:

• The folder ./lib/win/ contains the Visual Studio project file to build the static library.
• To compile the examples run the Developer Command Prompt for Visual Studio or Visual Studio x86(x64) Native Tools, change the folder to .examples/<Paper Name>/c++ and type

nmake -f Makefile_win

Once the library is built, you may go to the ./tests or ./examples folders to compile and run some examples.

The complete manual of how to use the existing code is presented in ./docs/Manual.pdf. The basic patterns of using DIRECTFN library can be found in the folder ./tests/basic. Here we briefly describe the main algorithm of computing the surface-surface singular integrals. In C++, you first #include "directfn_quad.h", if you need to work with quadrilateral elements, or #include "directfn_triag.h", if you need to work with triangles. Then you should define a "singular contour" SingularContour3xn according to the specific adjacency type with the proper number of points:

SingularContour3xn cntr;
cntr.set_points(r1, r2, r3, r4);

Here double[3] ri are coordinates of vertices of the considered elements in 3D--space. Note that the order of vertices for each case of adjacency must correspond to the rules defined below. Next, create an object of ST, EA or VA algorithm and use its interface instantiated by a ParticularKernel kernel type.

unique_ptr<Quadrilateral_ST<ParticularKernel>> up_quad_st(new Quadrilateral_ST<ParticularKernel>());

The type ParticularKernel is a C++ type which inherits the AbstractKernel class defined in directfn_kernel_base.h/cpp. The specific kernels implemented for quadrilaterals and triangles are discussed in details in the next sections. Now you should define the wavenumber k0 and the orders of Gauss-Legendre quadratures N1, N2, N3, N4, and assign your contour cntr with vertices to your object up_quad_st.

up_quad_st.set_wavenumber(k0);
up_quad_st.set_Gaussian_orders_4(N1, N2, N3, N4);
up_quad_st.set(cntr);

Now you are ready to calculate the surface-surface singular integral(s) by calling

up_quad_st.calc_Iss(); // Iss = Integral Surface-Surface

and use the obtained values.

const dcomplex * ref_val = up_quad_st->Iss();
// use ref_val somewhere

In case you need to recalculate these integrals for several contours or wave numbers we strongly recommend to do it as it is shown above: create an object of the Quadrilateral_ST(EA,VA) algorithm once and then use it for contour points or other parameters reset. This helps to avoid time-consuming memory allocation/deallocation related to creating and destroying the object. In case you need to compute the integral once, you can use a simpler interface, developed for Matlab scripts.

The folder ./examples contains the scripts to reproduce results, presented in paper [2]. For a given example there are two ways to execute it:

• Go to ./examples/EuCap2017_Examples/c++ or [`./examples/Full_Paper_Examples/c++] (/examples/Full_Paper_Examples/c++) folder and compile the C++ code:

make

or

nmake -f Makefile_win

if you are using nmake utility. then type the name of the executable file

./test_name

It will create a file Results_<test_name>.txt with timings and errors, and you can open Examples.ipynb notebook and visualize the results by executing the corresponding cell. Note that to run the .ipynb file you need ipython to be installed.

• The other way is to use Matlab scripts. To do this, you first need to build the mex interface to C++ functions by going to the ./mex folder and executing the build.m script. After that, you can go to the folder ./examples/EuCap2017_Examples/matlab/ or ./examples/Full_Paper_Examples/matlab/ and run any test_name.m script and it will do all the computations and produce the error plots and timings automatically.
• Note that if you're going to build mex files with one of the standart Windows compiler, e.g., provided by Visual Studio, you should build the static library with Windows compiler as well, i.e., using nmake.

[1] A. G. Polimeridis, F. Vipiana, J. R. Mosig, and D. R. Wilton, “DIRECTFN: Fully numerical algorithms for high precision computation of singular integrals in Galerkin SIE methods,” IEEE Trans. Antennas Propag., vol. 61, no. 6, pp. 3112–3122, Jun. 2013.

[2] A. A. Tambova, M. S. Litsarev, G. D. Guryev, and A. G. Polimeridis, "On the generalization of DIRECTFN for singular integrals over quadrilateral patches", IEEE Trans. Antennas Propag., (submitted), arXiv:1703.08146 [physics.comp-ph].

Copyright © 2016 Athanasios Polimeridis

DIRECTFN is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

DIRECTFN is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU GPLv3 for more details.

You should have received a copy of the GNU Lesser General Public License along with this program. If not, see http://www.gnu.org/licenses/.