Eigenvalues/singular values and fast PDE algorithms: acceleration, conditioning, and stability (12w5021)


(California Institute of Technology)

Michael Haslam (York University)

Mark Lyon (University of New Hampshire)

(Case Western Reserve University)


The Banff International Research Station will host the "Eigenvalues/singular values and fast PDE algorithms: acceleration, conditioning, and stability" workshop from June 24th to June 29th, 2012.

Partial Differential Equation (PDE) theory constitutes a cogent set of

theoretical and computational methods that enable qualitative and

quantitative understanding in vast areas of science and engineering,

including the fields of physics, chemistry, biology, economics and

ecology, amongst many others. While many high-quality tools are

currently available for the numerical solution of Partial Differential

Equations, a large number of important problems have remained

intractable, or nearly so, due to the shear scale of the computer

power their solutions require. Interestingly, most of the difficulties

that hinder applicability and/or performance of numerical methods

concern a certain mathematical obstacle (known to mathematicians as

unfavorable specral distributions) which has an impact across

disciplines and methodologies. With increasing computational power,

the ambitions to produce physically faithful numerical solutions have

been raised to exceedingly high levels; in recent years it has become

clear, however, that the advances in computer technology alone will not

enable accurate solution of complex scientific PDE problems. The

mathematical problems to be considered in this workshop lie at the

core of such difficulties. The participants of this workshop include

some of the most highly recognized international experts in the field.

We are thus confident the outcome of this workshop will help advance

significantly the state of the art in the field of computational

science, and will have a significant impact on science and engineering

in years to come.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).