Welcome to AFMM2Dlib’s Documentation!

About \(\texttt{AFMM2Dlib}\):

AFMM (Algebraic FMM) is an FMM implementation where the low rank approximations of appropriate matrix sub-blocks are formed in an algebraic fashion.

\(\texttt{AFMM2Dlib}\) is a library consisting of AFMM for kernels in 2D.

Low-rank approximation of the appropriate blocks is obtained using ACA. The domain is subdivided based on a KDTree. The algorithm has been parallelized using OpenMP.

The code is written in C++ and features an easy-to-use interface, where the user provides the following inputs:

• a kernel object which abstracts data of the matrix through a member function getMatrixEntry(int i, int j) which returns the entry at the \(i^{\mathrm{th}}\) row and \(j^{\mathrm{th}}\) column of the matrix.

• locations of nodes in the domain through an Eigen matrix loc

• the vector b to be multiplied to the matrix

Obtains \(A x\) at a cost of \(\mathcal{O}\left(N\right)\)

Doc Contents

Contents:

• Installation and Building
  • Downloading the Source
  • Dependencies
  • Installation
  • Testing
  • Building and Executing
• Tutorial
  • Setting Parameters in CMakeLists.txt
  • Running the program::
  • Creating a Derived Class of kernel:
  • Defining vector b:
  • Creating the Instance of AFMM:
• Benchmarks
  • Time Taken vs Tolerance
  • Time Taken vs Size of Matrix

Other Links

Learn more about \(\texttt{AFMM2Dlib}\) by visiting the

• Code Repository: http://github.com/sivaramambikasaran/AFMM2D

• Documentation: http://afmm2d.rtfd.io