A Finite Difference Approach to Pseudospectral Methods

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9706916 B. Fornberg Pseudospectral (PS) methods - a high-accuracy alternative to finite difference (FD) and finite elemnt methods - are particularly effective for solving convection-dominated PDEs over long times and in relatively simple geometries. Both the algorithms themselves and their analysis have usually been closely tied to expansions in different classes of orthogonal functions. The recent book "A Practical Guide to Pseudospectral Methods" (by the present investigator) notes that a large body of generalizations, enhancements and insights can be gained by viewing PS methods instead as special cases of FD methods. These opportunities will now be explored further, in particular with the aim of combining the PS approach with domain decomposition for time-dependent computational electromagnetics. Pseudospectral (PS) methods were first proposed in the early 1970's (in connection with meteorology and turbulence modeling). They are now routinely used in many fields such as nonlinear wave motions, weather forecasting, fluid mechanics, computational chemistry, and with time-domain computational electromagnetics (TD CEM) emerging as a new and potentially major application area. This present investigation will explore how a series of new leads for PS methods can be developed further and then brought to bear on applications, in particular in the field of TD CEM. Such applications include simulations of the radar visibility of objects and of how electromagnetic fields are generated by/ interact with components on integrated circuits.