An introduction to numerical methods of pseudodifferential operators

Abstract

Pseudodifferential operators were introduced in the mid 1900s as a powerful new tool in the development of the theory of partial differential equations. More recently, it has been observed that these operators may form the basis for novel numerical techniques used in the analysis and simulation of physical systems including wave propagation and medical imaging, as well as for advances in signal processing. This course will focus on the numerical implementations of pseudodifferential operators and practical applications. Of particular interest are: the variety of ways to implement these operators, including via fast transforms, decomposition into product-convolution operators, Gabor multipliers, and wavelet transform; speed of implementations; relation to asymptotic expansions; real experience with numerical implementations including in geophysical applications. © 2008 Springer-Verlag Berlin Heidelberg.