Research
Papers
Submitted
Odd behaviour of even geometries: an explanation for superconvergent geometric consistency errors
Cubature from rational approximation
A High-Order Fast Direct Solver for Surface PDEs on Triangles
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
Global Polynomial Level Sets for Numerical Differential Geometry of Smooth Closed Surfaces
A Note on the Rate of Convergence of Integration Schemes for Closed Surfaces
High-Order Numerical Integration on Regular Embedded Surfaces
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, with high-order surface quadrature, enclosed volume computation, and geometric invariant integration using an Algoim/C++ backend.