## 2019

#### Abstract Title

Sparse Matrix Operations and Finite Element Assembly

#### Presenter/Author/Student Information

The project described was supported by an Idaho State University Career Path Internship.

#### Abstract

A partial differential equation (PDE) is an equation relating functions of multiple variables, and their derivatives. These equations arise naturally in many science and engineering applications. PDEs, however, are often very difficult or impossible to solve directly. The Finite Element Method (FEM) provides a way to obtain a numerical approximation of the solution to a PDE. This method involves converting the continuous problem into a discrete problem by assembling linear system of equations. Since the matrix associated with the linear system is always sparse (mostly zero), we can improve the efficiency of the computer implementation by only storing the nonzero values in computer memory. In this project, we created an implementation of the FEM (using C), which assembles and solves the linear system associated with a PDE. This implementation makes use of sparse matrix algorithms such as addition, multiplication, and transposition.

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Sparse Matrix Operations and Finite Element Assembly

A partial differential equation (PDE) is an equation relating functions of multiple variables, and their derivatives. These equations arise naturally in many science and engineering applications. PDEs, however, are often very difficult or impossible to solve directly. The Finite Element Method (FEM) provides a way to obtain a numerical approximation of the solution to a PDE. This method involves converting the continuous problem into a discrete problem by assembling linear system of equations. Since the matrix associated with the linear system is always sparse (mostly zero), we can improve the efficiency of the computer implementation by only storing the nonzero values in computer memory. In this project, we created an implementation of the FEM (using C), which assembles and solves the linear system associated with a PDE. This implementation makes use of sparse matrix algorithms such as addition, multiplication, and transposition.