A computational fluid dynamics
simulation with finite elements (USEMe library)
Finite element methods (FEM) are versatile and efficient techniques
for approximating PDEs. They come in many types and flavors, but
the focus in our department is towards modern, high-order fine
element methods such as discontinuous Galerkin, and
spectral element methods which are Dr. Warburton's
specialties. Ph.D. student Tommy Binford works on new finite element
methods.
Highlights
Two high-order adaptive finite element libraries developed in
part by Dr Warburton, are available,
- USEMe: A MATLAB
unstructured spectral element library released under a public
domain license.
- Sledge++: A C++ discontinuous Galerkin finite element
library, soon to be released to the public
domain.
Scattered field computed with an
integral equation method.
Reformulating a partial differential equation in terms of an integral
equation enables the development of highly efficient and accurate
numerical methods for a wide variety of important scientific and
engineering applications. For example, integral equation methods are
often used in the computation of wave propagation and scattering. Such
problems arise in radar and remote sensing, medical and biological
imaging, laser-driven fusion, electron and neutron diffraction, etc.
Traditional discretization methods discretize the space surrounding the
scattering obstacles, whereas integral equation methods require only a
discretization of the surface of the scatterer. For example, in the case
of radar scattering by an airplane, an integral equation method only
requires the discretization of the airplane's fuselage. This makes
integral equation methods very efficient for computing scattered fields:
it is much cheaper to solve a 2D problem (on the airplane's fuselage) than
a 3D problem (in the space surrounding it). Dr
Hyde is an specialist in
this type of methods.
