Papers

• A High-Order Fast Direct Solver for Surface PDEs on Triangles. (Submitted)

  Note: The triangular version is more flexible for complex geometries, but if a structured mesh is available, the quadrilateral-based HPS is still more efficient. In particular, derivatives are more expensive to compute on triangles, and the condition number grows faster.
  The companion paper arXiv:2512.24456 gives the broader framework, including a quadrilateralization approach and an extension to PDEs on evolving surfaces.

• High-Order Integration on Regular Triangulated Manifolds Reaches Super-Algebraic Approximation Rates through Cubical Re-parameterizations . Joint with Oliver Sander and Michael Hecht. SIAM Journal on Numerical Analysis(SINUM)
• Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces . Joint with Sachin K. Thekke Veettil, Uwe Hernandez Acosta, Ivo F. Sbalzarini, and Michael Hecht. SIAM Journal on Computing (SICOMP).
• A Note on the Rate of Convergence of Integration Schemes for Closed Surfaces . Joint with Elima Shehu and Michael Hecht. Computational and Applied Mathematics, Springer.
• High-Order Numerical Integration on Regular Embedded Surfaces . Joint with Michael Hecht. Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2.