The talk will present the open-source convex optimisation solver Clarabel, an interior-point based solver that uses a novel homogeneous embedding technique offering substantially faster solve times relative to existing open-source and commercial interior-point solvers for some problem types. This improvement is due to both a reduction in the number of required interior point iterations as well as an improvement in both the size and sparsity of the linear system that must be solved at each iteration. For large-scale problems we employ a variety of additional techniques to accelerate solve times, including chordal decomposition methods, GPU sub-solvers, and custom handling of certain specialised cones. The talk will describe details of our implementation and show performance results with respect to solvers based on the standard homogeneous self-dual embedding.

This talk is hosted by Rutherford Appleton Laboratory and will take place @ Harwell Campus, Didcot, OX11 0QX

The Whitney forms on a simplicial triangulation are piecewise affine differential forms that are dual to integration over chains.  The so-called blow-up Whitney forms are piecewise rational generalizations of the Whitney forms.  These differential forms, which are also called shadow forms, were first introduced by Brasselet, Goresky, and MacPherson in the 1990s.  The blow-up Whitney forms exhibit singular behavior on the boundary of the simplex, and they appear to be well-suited for constructing certain novel finite element spaces, like tangentially- and normally-continuous vector fields on triangulated surfaces.  This talk will discuss the blow-up Whitney forms, their properties, and their applicability to PDEs like the Bochner Laplace problem.