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2D periodic rheology simulation via boundary integral equations: 25 rigid neutrally-buoyant ellipses per unit cell in a shearing Stokes flow (with J. Wang, E. Nazockdast; JCP '21)
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Timings of our ARDC solver vs others,
for a 2nd-order oscillatory ODE with frequency λ,
via adaptive defect correction for the Riccati phase function
(with F. Agocs; SINUM '23).
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3D acoustic wave equation via high-order Volterra time-domain boundary integral equations: pulsed plane wave scattering from smooth cruller shape to 5-digit accuracy (with T. Hagstrom, L. Greengard; JCP '20).
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Fresnel scalar diffraction intensity from a hard-edged occulter,
to 12-digit accuracy, at 106 targets, in 0.05 s on a laptop.
The petal design is a "starshade" for exoplanet astronomy
(JATIS '21).
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Lower bounds on rate of exponential ill-conditioning of rectangular submatrices of the discrete Fourier matrix, using the Kaiser-Bessel window as an analytic tool (SIREV '22; this inspired a beautiful diagonal improvement by Shah & Urschel '26).
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Point excitation of 2D infinite periodic sound-hard polygon to 10-digit accuracy, modeling dispersive trapped waves at Mayan pyramid staircases (with F. Agocs; JCP '24).
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3D Stokes sedimentation (mobility) of 10000 rigid ellipsoids solved to 5-digit accuracy using one-body preconditioned method of fundamental solutions (with A. Broms and A.-K. Tornberg; JCP '25).
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3D Stokes flow lines solved near slender rigid bodies separated by 1/20 of their minor radius, computed to 10-digit accuracy using CSBQ (with D. Malhotra; JCP '24).
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