James Bremer

Associate Professor of Mathematics, University of California, Davis

My work is concerned with the development of efficient algorithms for scientific computing, particularly the solution of differential and integral equations. Some of my recent projects include:

• A highly effective algorithm for numerical solution of the variable coefficient Helmholtz equation in one dimension which runs in O(1) time (that is, time which is independent of the frequency of oscillations of the solutions).
• High-order methods for the discretization of integral equations given on surfaces with complicated geometry, particularly those with edges and corners.
• O(1) algorithms for the numerical evaluation of a large class of special functions, which includes the associated Legendre functions, generalized Laguerre polynomials, Jacobi polynomials, etc.
• Fast algorithms for applying special function transforms, including the spherical harmonic transform and Jacobi transform.

I am now developing an O(1) solver for the variable coefficient Helmholtz equation in two dimensions. More information about my research can be found here. Many of my software packages are available at my GitHub page.

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