Principal Numerical Analyst

This is not an applied engineering job. We are looking for a high end numerical analyst with unusually strong geometric intuition to join Blue Chips Research.

Most computational work starts after the mathematics has already been formalized: the operator is known, the equations are written down, and the job is to discretize, accelerate, precondition, approximate, or scale.
We are trying to compute things before the mathematical community has finished deciding what the right formal object is.

Our current work is focused on near-singular quadrature, boundary integral evaluation, and discrete representations of boundary operators in 3D computational physics
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We are particularly interested in candidates with strong experience in some combination of:

• hypersingular and near-singular quadrature
• boundary integral equations and layer potentials
• spectral inverse problems
• (H^{1/2}) and (H^{-1/2}) trace spaces
• fractional or pseudodifferential laplacian
• high-order approximation on curved surfaces
• judgement and taste on numerical conditioning and stability

Relevant backgrounds may include BEM, CFD, computational electromagnetics, reservoir simulation, or related areas. Ideal candidates will have a PhD in Mathematics, Computational Physics, Quantitative Finance, or similarly rigorous field, but we are open to exceptional candidates with less traditional backgrounds. The primary qualification is that you can demonstrate at least one of these things:

1) have made a novel structural contribution recognized by institutions like SIAM/NIST or by the open source community (pytential/mpmath-tier)

2) you have a reference from someone in (1) that can vouch for exceptional work you did

3) You can demonstrably compute something that we cannot and does not exist in the prior art.

You can fake a resume but even time and tuition can't forge convergence. This is a research position rather than a production solver or computational engineering role. The emphasis is on understanding the numerical and analytic structure of the problem: which effects are genuinely singular, which are representational, which aspects are local or global, and what finite structure is being preserved by the discretization.

We would be especially interested in someone who has worked on problems where a stable numerical phenomenon preceded a satisfactory mathematical explanation.