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

University essay from Lunds universitet/Matematik LTH

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.

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