GIMC SIMAI Young 2026

Session

MS04.2 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

4 Jun 2026, 11:15

Pisa

23. Adaptive Isogeometric Analysis of the Cahn--Hilliard Equation with THB-splines

Lucas Venta Viñuela (University of Pavia)

04/06/2026, 11:15

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

Isogeometric Analysis has been proven to be a suitable tool for the discretization of higher-order formulations describing phenomena like brittle fracture or phase separation in fluid mixtures [1,2]. In this context, phase-field models constitute a convenient approach to model sharp interface problems, since they incorporate a continuous field variable --the field order parameter-- to describe...

118. A Cahn–Hilliard Equation-based Tumor Growth Model with Nutrient Coupling

Dhiraj Sanghavijay Bombarde (Department of Civil Engineering and Architecture, University of Pavia, Italy)

04/06/2026, 11:30

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

Predicting tumor dynamics in biological systems under physiologically relevant conditions remains a challenging problem for mathematical and computational modeling. Among the various approaches proposed to describe tumor dynamics, phase-field (diffuse-interface) formulations provide an attractive continuum modeling framework to capture the spatiotemporal evolution of interfaces separating...

155. Parameter optimization for the Cahn-Hilliard equation with applications to tumor growth models

Leonardo Beretta (Università di Pavia)

04/06/2026, 11:45

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

The Cahn-Hilliard equation is used to describe the dynamics of two phases interacting across a thin region known as the interface. This framework naturally lends itself to the formulation of tumor growth models.
In this work we deal with parameter estimation for a phase-field model of tumor evolution coupled with nutrient dynamics. The mathematical model consists of a Cahn-Hilliard type...

20. Local h-, p-, and k-Refinement Strategies for the Shifted Boundary Method with THB-Splines

Christoph Hollweck (OTH Regensburg/ TU München)

04/06/2026, 12:00

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

Trimming and immersion techniques have become standard tools for handling complex geometries in isogeometric analysis (IGA). By decoupling the physical domain from the computational background mesh, mesh generation is simplified compared to body-fitted approaches. However, this embedding strategy introduces numerical challenges, including ill-conditioning due to small cut elements.
The...

39. A p-adaptive high-order polytopal method for modelling neuronal electrophysiology

Caterina B. Leimer Saglio (Politecnico di Milano)

04/06/2026, 12:15

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

Traveling wave-like phenomena arise in a wide range of biological processes, including electrical signal propagation in the nervous system and brain tissue. Accurately simulating these phenomena poses significant numerical challenges, as sharp and rapidly moving wavefronts require high spatial and temporal resolution to be properly captured. Such requirements often lead to prohibitive...

175. A high–order time and space–accurate method for the explicit dynamics of geometrically exact beams

Giulio Ferri (Universittà degli Studi di Firenze)

04/06/2026, 12:30

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

In this contribution, we propose a high–order time and space–accurate isogeometric collocation (IGA-C) method for the explicit dynamics of geometrically exact beams [1]. While high–order accuracy in space is a well established feature of IGA-C for both explicit and implicit dynamics of geometrically exact beams [2, 3], time accuracy is still restricted to second–order. For some applications...