FEM-CPP-Building-Blocks

Introduction

This repository contains C++ classes intended to allow rapid building and construction of Finite Element code. Implementation is split into two main classes:

• C_Matrix_Dense - Stores a matrix as a vector in Row-Major format. Supports all standard matrix manipulations, including addition, subtraction, matrix and scalar multiplication and transposition. Size is determined at initialization/assignment; dynamic resize is not allowed. Use C_Matrix_Dense to construct individual elements. C_Matrix_Dense is now set up as template class, and allows specification of the type of data it holds, as, for example, C_Matrix_Dense<int> or C_Matrix_Dense<double>.
• C_Matrix_Sparse - Stores a matrix as a vector of linked lists, retaining only non-zero (and accessed) elements. By default, stores in COO format; use this for initialization of the object. If needed, convert to CSR representation, by calling C_Matrix_Sparse::convert_to_CSR(). Use C_Matrix_Sparse to assemble element matrices into a lightweight sparse matrix in formats suitable for use with different solver libraries.

Overloaded output-stream (<<) operator allows user-friendly viewing of matrix contents for each class. C_Matrix_Sparse::print_contents() displays non-zero elements only.

Installation

FEM-CPP-Building-Blocks is a header-only library. Installation should be as simple as cloning the repository and using a suitable compiler. Currently, this repository is tested and known to work with g++17.

FEM-CPP-Building-Blocks is designed to be used as for construction of solver-agnostic objects, flexible enough to grow with a finite element research project. Solver interfaces are stored separately so that base classes do not have dependencies on external libraries unless they are used.

Implementation

Demo scripts are included that show how to construct matrices and display to the terminal. The syntax is simple, and is designed to be MATLAB-like where possible.

Basic Assignment to Matrices

// Stored matrix { {1, 2}; {3, 4} }
// Enter in Row-Major ordering
C_Matrix_Dense<int> A(2,2) = {1, 2, 3, 4}; 

C_Matrix_Dense<int> B(2,2);
B = -A.T(); // Set B equal to negative of A-transpose.

Write to Sparse Matrix

C_Matrix_Sparse C(6,6); // Default NNZ = 0;

// Store Contents of Dense Matrix on rows 4:5 and columns 3:5 (C++ is zero-indexed)
C.add_matr(B, {3,4}, {2, 3}); 

Display to Terminal

std::cout << A;
std::cout << B;
std::cout << C;

Contributors

• Dominic Jarecki
• Bensingh Dhas

Acknowledgements

In association with:

CONTINUUM MECHANICS @ TAMU

Center of Innovation in Mechanics for Design and Manufacturing (CIMDM)