Numerical Methods
List of researchers in CAMS working on problems related to Numerical Methods:
Bhattacharjee,
Bukiet,
Elmer,
Goldman,
Goodman,
Horntrop,
Jiang,
Kondic,
Luke,
Ma,
Matveev,
Michalopoulou,
Moore,
Muratov,
Papageorgiou,
Petropoulos,
Rosato,
Siegel,
Tao,
Wang,
Yoo,
Young.
Given the rapid development of the power of computers in recent
decades, the use of computation as a means of scientific inquiry
has also greatly increased and now is ubiquitous in most areas
of applied mathematics. CAMS researchers are involved in all
aspects of this scientific revolution from the development
of new, more efficient and accurate numerical algorithms to the creation
of computational packages for use by researchers throughout
the world. The computational work of CAMS researchers is
supported by state of the art facilities including
numerous workstations and a 134 processor
cluster.
Virtually every CAMS member uses computation in some aspect of
their research. Some of the specific computational tools that
are being used and developed by CAMS researchers are described below.
Boundary integral methods are being used to study moving
interfaces in materials science and fluid dynamics.
Computational solutions of nonlinear
partial differential equations
are used in studies of the formation of finite-time
singularities in aerodynamic and interfacial problems.
A wide variety of finite difference methods for ordinary
and partial differential equations, often in conjunction with
iterative solvers and conjugate gradient methods,
are used in studies of advection-diffusion
problems, wave propagation, blood circulation, the visual
cortex, as well as synaptic function
and intracellular spatio-temporal calcium dynamics.
Level set methods are used to study interfaces in materials.
Novel techniques for differential
difference equations are also used to better understand materials.
Convergence of fast multipole methods is analyzed
and these methods are used to study wave propagation.
Novel techniques to remove spurious reflections of waves at
computational boundaries are being developed.
Signal detection and estimation techniques rely upon
global optimization techniques used and developed by CAMS
researchers.
Finite element methods are used to study mechanical systems;
the immersed boundary method is being developed
and refined in order to improve
computational accuracy and efficiency near interfaces.
Stochastic computation also receives a great deal of attention by
CAMS researchers. Monte Carlo methods based upon the principles
of statistical mechanics are used in studies of granular materials.
Monte Carlo simulation is used to
study molecular biology and bioinformatics.
Stochastic models of sedimentation are being developed and refined
through a combination of analysis and simulation.
Markov Chain Monte Carlo methods are used in studies
in statistics and biostatistics.
Simulations taking advantage of variance reduction techniques
are being used to study the effects
of stochastic perturbations on solitons.
New computational techniques for stochastic partial differential
equations based upon spectral methods are being developed and
applied to multiscale models of surface processes.
The rest of this page contains links to examples of the research projects
that have been recently considered by the CAMS members. The links to individual
faculty web pages that contain more information can be found at the top of
this page.