GIMC SIMAI Young 2026

Session

MS04.3 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

4 Jun 2026, 14:00

Pisa

52. A fast Poisson solver for isogeometric analysis

Mattia Tani

04/06/2026, 14:00

MS04 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

Consider the Poisson problem on a $d$-dimensional cube. It is well-known that, if the problem is discretized with linear finite elements on a uniform tensor product mesh, the resulting sti ness matrix can be diagonalized using the Fast Fourier Transform. This fact can be exploited to solve the linear system yielding $O(N \log N)$ complexity, where N represents the number of degrees of freedom....

14. Stabilization-free Virtual Elements: the general order method

Davide Fassino (Politecnico di Torino)

04/06/2026, 14:15

MS04 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

The Virtual Element Method (VEM) is a polygonal finite element method characterized by geometric flexibility and has therefore been applied to a wide range of engineering problems. Despite its popularity, some difficulties arise when dealing with strongly nonlinear and anisotropic problems, mainly due to the presence of a non-consistent stabilization term that needs to be introduced to ensure...

58. Benchmarking stabilized and self-stabilized p-virtual element methods with variable coefficients

Fabio Credali (King Abdullah University of Science and Technology)

04/06/2026, 14:30

MS04 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

Virtual Elements (VEM) [1] generalize the Finite Element Method, allowing the discretization of complex geometries through general polytopal meshes.

The discrete space, which includes polynomials to ensure accuracy, is implicitly defined, as shape functions are solutions of a local PDE that is typically not solved. The discrete problem is constructed via polynomial projections, and...

64. Preconditioning the mass matrix for isogeometric immersed method

Giovanni Varetto (Università Milano-Bicocca)

04/06/2026, 14:45

MS04 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

The mass matrix arising from the immersed isogeometric method is ill-conditioned due to the presence of severely trimmed elements in the computational domain, that is, elements of the mesh that only partially overlap with the domain of interest. We propose a preconditioning strategy based on the Additive Schwarz method.
Firstly, in contrast with existing methods, we use a preconditioner with...

133. Anisotropic Refinement with Decoupled Patchwork B-Splines and Bézier Extraction

Andreas Grendas (TU Graz)

04/06/2026, 15:00

MS04 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

Classical THB-spline refinement in isogeometric analysis relies on nested tensor-product spaces, which limits its efficiency for strongly directional solution features. This work presents an anisotropic refinement framework based on decoupled patchwork B-splines (DPB-splines), enabling patch-wise and directionally selective refinement while preserving standard element-wise assembly. The...