Papers

Submitted

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

  This triangular formulation is designed for complex geometries. For structured meshes, the quadrilateral HPS formulation remains more efficient. The companion work arXiv:2512.24456 gives the broader framework, including quadrilateralization and evolving surfaces.

Published

• High-Order Integration on Regular Triangulated Manifolds Reaches Super-Algebraic Approximation Rates through Cubical Re-parameterizations.
  With Oliver Sander and Michael Hecht. SIAM Journal on Numerical Analysis.

• Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces.
  With Sachin K. Thekke Veettil, Uwe Hernandez Acosta, Ivo F. Sbalzarini, and Michael Hecht. SIAM Journal on Scientific Computing.

• A Note on the Rate of Convergence of Integration Schemes for Closed Surfaces.
  With Elima Shehu and Michael Hecht. Computational and Applied Mathematics.

• High-Order Numerical Integration on Regular Embedded Surfaces.
  With Michael Hecht. Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2.

Software

• pysurfacefun
  High-order discretizations and fast direct solvers for PDEs on smooth surfaces.

• surfgeopy
  Surface integral approximation over smooth embedded manifolds.

• surfpy
  Spectral surface integration on embedded manifolds.

• minterpy-levelsets
  Numerical differential geometry on smooth surfaces via global polynomial level sets.
  Recently upgraded with high-order surface quadrature, enclosed volume computation, and geometric invariant integration using an Algoim/C++ backend.

PhD Thesis

Spectral Discretizations on Surfaces: High-Order Methods for Integration and PDE Solvers.
Technische Universität Dresden (2026) (supervised by Oliver Sander \& Michael Hecht)