We derive the dynamics of harmonic components for incompressible inviscid fluids, which has previously been overlooked in the vorticity-streamfunction formulation for Euler equations. We elucidate the physical laws associated with the new equations and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology.
This is a comprehensive course for graphics researchers to fill the gap between their undergraduate curriculum of multivariable calculus and cutting-edge graphics research. We use relevant examples from computer graphics to illustrate the theory of exterior calculus leading to advanced topics including continuum mechanics, fluid dynamics, and geometric optimizations.
We present a method for solving the wave equation on the entire infinite domain using only finite computation time and memory. We perform wave simulations in infinite spacetime using a finite discretization of the bounded spacetime with no additional loss of accuracy introduced by the Kelvin transformation.
We simulate Euler equations for inviscid fluids by using a novel formulation based on covectors. This new formulation is an entirely velocity-based method in the vein of advection-projection methods while emulating vortex methods. This allows for capturing more intricate vortex dynamics and reducing dissipation of energy with low computational overhead.
We solve infinite-domain simulation problems by applying the Kelvin transform. The transformation turns infinite-domain PDEs into bounded-domain ones via a domain inversion and a singularity factorization.
June 2nd 2023: Talk on Covector Fluids paper at Pixel Cafe at UCSD CSE department. (In-person)
April 22nd 2023: Talk on Covector Fluids paper at Southern California Fluids Conference. (In-person)
February 28th 2023: Talk on Covector Fluids paper at Geometric Mechanics at UCSD Math department. (In-person)
November 3rd 2022: Talk on Covector Fluids paper at joint oceanography seminar at UCSD Scripps Institution of Oceanography. (In-person)
August 10th 2022: Talk on Covector Fluids paper at SIGGRAPH 2022. (In-person) recording here
August 4th 2022: Talk on Covector Fluids paper at Stanford University. (In-person)
June 9th 2022: Talk on Covector Fluids paper at Visual Computing Center's retreat. (In-person)
June 7th 2022: Discussion on Covector Fluids paper at McGill Univeristy. (Remote)
June 2nd 2022: Talk on Covector Fluids paper at University of Waterloo Computer Graphics Lab (CGL). (Remote)
May 10th 2022: Talk on Covector Fluids paper at SideFX Software. (Remote)
September 24th 2021: Talk on Kelvin Transform paper at Toronto Geometry Colloquium (TGC). (Remote) recording here
August 11th 2021: Talk on Kelvin Transform paper at SIGGRAPH 2021. (Remote) recording here
Throughout my studies, I've managed to intern at various places with a focus on my passion for computer graphics, animation, and gaming.