Math 270E: Assignment 5

Assigned Wednesday, Oct. 21, 2008, due Wednesday, Oct. 28, 2008

In this assignment you will create a 2D Fast Poisson solver using FFTW based 2D discrete sin transform routines.

Additional files you will need for this assignment :

The FFTWinterface repository at https://www.math.ucla.edu/~anderson/270eSupport/
FFTW library routines (see below for details)

In the FFTWinterface repository are the following files:

fftw3_sin1d.h fftw3_sin1d.cpp	C++ interface to the FFTW 1-dimensional sin transform routines.
fftw3_sin2d.h fftw3_sin2d.cpp	C++ interface to the FFTW 2-dimensional sin transform routines.
fftw3_sin1dTest.cpp fftw3_sin2dTest.cpp	Test codes for 1-dimensional and 2-dimensional sin transform routines.
LaplaceOp1dD.h LaplaceOp1dD.cpp	1D Laplace operator routines. Both the forward and inverse operator (the latter being computed using the 1-dimensional sin transform).
LaplaceOp1dDTest.cpp	Test codes for 1D Laplace operator routines.

[1] Download the FFTWinterface codes. Obtain and install the FFTW libraries -- see Obtaining FFTW Libraries for details.

[2] Test your installation by compiling and then running one or more of the test codes in FFTWinterface. To be successful, you will have to take additional steps to include the fftw3 routines.

On Windows Machines:

You will need to

add to the include path for your project the directory containing the dll's since it also contains the required fftw3.h header file.
add the import library file, libfftw3-3.lib, to your project either by
- Adding the libfftw3-3.lib file explicilty to your project. The file chooser won't show .lib files by default, so you'll need to specify *.* to be able to see it. (sample screen shot) After adding it, hit "No" to the request to create a specific build rule.
  
  or
- Specifying the location of the directory containing the .lib file in the project property Configuration_Properties->Linker->General->Additional Include Directories (sample screen shot) and the library file libfftw3-3.lib in the project property Configuration_Properties->Linker->Input->Additional Dependencies (sample screen shot)
add the following PATH specification to the project propery Configuration_Properties->Debugging->Environment

PATH=%PATH%;Path to the folder containing libfftw3-3.dll

Here Path to the folder containing libfftw3-3.dll is the location of the folder containing libfftw3-3.dll (sample screen shot). If you used the standard MS Windows "extract all" option to unzip the file containing the dll's then this will be the path specifying the folder fftw-3.1.2-dll (note that it is "-dll" in the folder name and not ".dll").

If the PATH is not set correctly, when you run the program you'll get an error message indicating that the file libfftw3-3.dll can't be located and suggesting you re-install the program (screen shot). This error message is not indicating the right procedure to fix the problem!

UCLA Math Unix/Linux machines and other Unix/Linux machines where fftw3 libraries were pre-installed:
To use the libraries, you just need to link to the fftw3 library, e.g. add -lfftw3 to your compilation/linking command. (It's a small "ell" and not a 1, before fftw3).

On Unix/Linux machines where you have installed the fftw3 libraries:
To use the libraries, you need to specify the directory where you installed fftw3 library files and the name of the fftw3 library by adding

-L pathToLibFileDirectory

and

-lfftw3

to your compilation/linking command. (It's a small "ell" and not a 1, before fftw3). The "-L" option indicates to the compiler the directory where the library files are found.

[3] Write and then test a routine that uses the 2-dimensional sin transform routines to solve the discrete five-point Laplace equation with Dirichlet boundary conditions.

What You Should Turn In

A listing of your routine in [3] and a short written description of the tests that you performed in order to verify that your routines are working properly.