CBMS Conference: Algorithms for solving elliptic PDEs on modern computers---fast direct solvers, randomized methods, and high order discretizations,

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The award supports an NSF/CBMS regional conference that will be held at Dartmouth College in June of 2014 on the topic of so called "fast methods" for numerically solving linear partial differential equations (PDEs). This field of research has recently seen very rapid progress, and the purpose of the conference is to introduce recent results to junior researchers, and to engage them with current research. In particular, the conference will describe (1) new "direct" (as opposed to "iterative") solvers that in a single sweep construct an approximate solution to the equation under consideration, (2) new randomized methods for accelerating certain linear algebraic computations, and (3) the interplay between direct solvers and high-order discretization techniques that allow the solution of PDEs to ten digits of accuracy or more, even on complicated geometries.The broader motivation for the research to be discussed during the conference is the growing importance of computational simulations of physical phenomena in science and engineering. The ability to perform rapid virtual experiments rather than real (expensive) ones is a key driver of technological progress. While more powerful computers are important, development of efficient numerical algorithms that run well on modern hardware is equally crucial. The CBMS conference supported will disseminate knowledge about newly developed powerful algorithms that are designed from the ground up to minimize communication, which is emerging as the most important computational bottleneck. The conference will in addition to traditional lectures also give participants an opportunity for hands-on computational experimentation using tutorial style software. The lectures will be recorded and will be posted online along with the lecture slides, and the tutorial software. A monograph will be produced to create an integrated set of resources that will maximize the impact and reach of the conference. This project will be jointly supported by the Infrastructure Program and the Computational Mathematics Program within the Division of Mathematical Sciences.