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Creating Visual Effects by Solving Partial Differential Equations in Real-Time

Ornstein Mecklenburg, Kasper LU (2014) In Bachelor's Theses in Mathematical Sciences FMNL01 20141
Mathematics (Faculty of Engineering)
Abstract
The goal of this bachelor thesis is to create visual effects by solving partial differential equations (PDEs). The visual effects should be dependent on the input from music and the PDEs are solved in real-time. Creating visual effects can be done in many different ways and the reason for using PDEs is that they model natural phenomena which is appealing to the human eye. Focus will be on studying three different finite difference methods and one spectral method. Fast implementations are essential and by using multigrid techniques as well as the fast Fourier transform this can be achieved. In order to determine which method is suitable, we compare execution times as well as accuracy in time and space for different initial values. The final... (More)
The goal of this bachelor thesis is to create visual effects by solving partial differential equations (PDEs). The visual effects should be dependent on the input from music and the PDEs are solved in real-time. Creating visual effects can be done in many different ways and the reason for using PDEs is that they model natural phenomena which is appealing to the human eye. Focus will be on studying three different finite difference methods and one spectral method. Fast implementations are essential and by using multigrid techniques as well as the fast Fourier transform this can be achieved. In order to determine which method is suitable, we compare execution times as well as accuracy in time and space for different initial values. The final conclusion is that the spectral method is superior for the heat equation which was studied in the report. (Less)
Please use this url to cite or link to this publication:
author
Ornstein Mecklenburg, Kasper LU
supervisor
organization
course
FMNL01 20141
year
type
M2 - Bachelor Degree
subject
keywords
Partial Differential Equations, Real-Time, Python, Visual Effects
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUTFNA-4001-2014
ISSN
1654-6229
other publication id
2014:K4
language
English
id
4499472
date added to LUP
2014-07-04 17:34:16
date last changed
2015-12-14 13:32:15
@misc{4499472,
  abstract     = {The goal of this bachelor thesis is to create visual effects by solving partial differential equations (PDEs). The visual effects should be dependent on the input from music and the PDEs are solved in real-time. Creating visual effects can be done in many different ways and the reason for using PDEs is that they model natural phenomena which is appealing to the human eye. Focus will be on studying three different finite difference methods and one spectral method. Fast implementations are essential and by using multigrid techniques as well as the fast Fourier transform this can be achieved. In order to determine which method is suitable, we compare execution times as well as accuracy in time and space for different initial values. The final conclusion is that the spectral method is superior for the heat equation which was studied in the report.},
  author       = {Ornstein Mecklenburg, Kasper},
  issn         = {1654-6229},
  keyword      = {Partial Differential Equations,Real-Time,Python,Visual Effects},
  language     = {eng},
  note         = {Student Paper},
  series       = {Bachelor's Theses in Mathematical Sciences},
  title        = {Creating Visual Effects by Solving Partial Differential Equations in Real-Time},
  year         = {2014},
}