Numerical approximation of the Electroconvection
Numerical approximation of surface quas-geostrophic flow
Numerical approximation of the solution to the integral laplacian problem on a sphere with unitary right hand side using the representation $$\int_{\mathbb R^d} \int_{\mathbb R^d} \frac{(u(x)-u(y))(v(x)-v(y))}{|x-y|^{d+2s}} = \frac{2\sin(\pi s)}{\pi} \int_0^\infty t^{2(1-s)}(-\Delta(I-t^2\Delta)^{-1} u,v)_{L_2(\Omega)} \frac{dt}{t}$$
Biomembrane with an area and volume of an 5x5x1 ellipsoid (left), 7x7x1 ellipsoid (center) and 8x1x1 ellipsoid (right)
Numerical Simulation of the Kaye effect
Undergraduate students enrolled in our program are welcome to contact me to participate on current reasearch projects.
Graduate students already enrolled in our graduate program and interested in the theoretical and/or computational aspects of
High dimensional approximations in the context of parametric PDEs
or
Numerical Simulation of bilayer actuators
To be well prepared for research you should consider the following recommendation on the classes to take
Applied Math / Numerical Analysis and Real Analysis
Differential Geometry, Graph Theory or Combinatoric
Any special topic class in numerical analysis, approximation theory or PDEs, MTH661, MTH 676, MTH611, MTH 612.