Research Interests

Most of my work has been devoted to building mathematical tools for the design of asymptotically fast, rapidly convergent numerical methods with applications in forward and inverse scattering, potential theory, fluid and molecular dynamics, electrical engineering, and a variety of other areas in the applied sciences. In the development of computational techniques, one of the dominant influences has been Moore's law, stating that the speed of computer hardware is roughly doubled every 18 months; the increase in available memory, disk space, and so on has been even faster. Under these conditions, small differences in the efficiency of algorithms become irrelevant; what matters is the asymptotic behavior of the scheme (in terms of both CPU time and memory requirements) as the size of problems to be solved increases. Another consequence of the increase in computational power is that for the first time, it is becoming possible to solve real-world scientific and engineering problems with high precision and reliability; this calls for rapid (so-called high-order) convergence, robust behavior in adaptive environments, and simple accuracy control.

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Primary Section

Section 32: Applied Mathematical Sciences