Low-complexity Algorithms to Solve Partial Differential Equations
Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
group
Campus
Daytona Beach
Authors' Class Standing
Jose R. Gonzalez -Senior Isaac X. LaRosee- Senior
Lead Presenter's Name
Jose R. Gonzalez
Lead Presenter's College
DB College of Arts and Sciences
Faculty Mentor Name
Sirani Perera
Abstract
The Discrete Fourier Transform (DFT) has plethora of applications in mathematics, physics, computer science, and engineering. Fast Fourier transform (FFT) is an algorithm used to efficiently compute DFT and its inverse. In this work, we obtain solutions to fundamental partial differential equations (PDEs) using fast, i.e. FFT-like, algorithms. In particular, solutions to the Heat equation, Wave equation, and Schrödinger equation are explored using low-complexity algorithms in connection to the sparse factorization of matrices. We compare the complexity in solving the PDEs using the standard Fourier transform in continuous domains vs the proposed fast algorithms in discrete domains. We also analyze the accuracy of the solutions and present simulation results based on the proposed algorithms.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
Yes, Student Internal Grants
Low-complexity Algorithms to Solve Partial Differential Equations
The Discrete Fourier Transform (DFT) has plethora of applications in mathematics, physics, computer science, and engineering. Fast Fourier transform (FFT) is an algorithm used to efficiently compute DFT and its inverse. In this work, we obtain solutions to fundamental partial differential equations (PDEs) using fast, i.e. FFT-like, algorithms. In particular, solutions to the Heat equation, Wave equation, and Schrödinger equation are explored using low-complexity algorithms in connection to the sparse factorization of matrices. We compare the complexity in solving the PDEs using the standard Fourier transform in continuous domains vs the proposed fast algorithms in discrete domains. We also analyze the accuracy of the solutions and present simulation results based on the proposed algorithms.