Many geometry-processing pipelines reduce to large sparse linear systems and eigenvalue problems. Direct factorisation does not scale to millions of degrees of freedom, so iterative methods, hierarchical representations, and multilevel preconditioners become essential.
My contributions include a geometric multigrid solver tailored to curved surface meshes (SIGGRAPH 2023), hierarchical subspace iteration for Laplace–Beltrami spectra (ACM TOG 2022), and fast approximation schemes for eigenproblems (CGF / SGP 2018). Together they address both “solve once accurately” and “approximate many times interactively” regimes.
Geometric multigrid solvers on surfaces
Multigrid methods combine smoothing on fine meshes with coarse-grid correction to achieve near-linear complexity for elliptic problems. Adapting this machinery to curved simplicial surfaces requires careful transfer operators and hierarchy construction so that curvature and irregular connectivity do not degrade convergence.
Related publications
Hierarchical subspace iteration
For eigenproblems, we iterate within nested subspaces tied to mesh resolution, focusing computational effort where it changes the spectrum most. This is complementary to multigrid for linear solves and targets the bottleneck of many eigenmodes on fine triangulations.
Related publications
Linear solvers & fast spectral approximation
FastSpectrum-style approximation prioritises low modes that dominate perceptual and physical behaviour, using compact operators that can be assembled and applied cheaply — useful when designers need immediate feedback during editing sessions.
Related publications
All papers in this area
Numerical / solver-focused work; newest first.