Related papers: Skeleton-stabilized IsoGeometric Analysis: High-re…
We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid-structure interaction (FSI) phenomena for air blast. We aim to develop a practical computational…
Motivated by the search for solvable string theories, we consider the problem of classifying the integrable bosonic 2d $\sigma$-models. We include non-conformal $\sigma$-models, which have historically been a good arena for discovering…
This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
In this paper, we consider up-to-date and classical Finite Element (FE) stabilized methods for time-dependent incompressible flows. All studied methods belong to the Variational MultiScale (VMS) framework. So, different realizations of…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…
We introduce and analyze a Statically Condensed Iterated Penalty (SCIP) method for solving incompressible flow problems discretized with $p$th-order Scott-Vogelius elements. While the standard iterated penalty method is often the preferred…
We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…
Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, numerical methods based on interface models are intensively…
We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface…
We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with…
The direct-forcing immersed boundary method (DF-IBM) algorithm previously developed by the authors is extended by coupling the Navier-Stokes equations with the Newton-Euler equations for rigid body dynamics within the DF-IBM framework. This…
Stability analysis is performed on surface quasigeostrophic systems subjected to a Kolmogorov-type "shear force" on the boundaries using linear and nonlinear approaches. For a SQG system of semi-infinite depth forced on the upper boundary,…
Most variational forms of isogeometric analysis use highly-continuous basis functions for both trial and test spaces. For a partial differential equation with a smooth solution, isogeometric analysis with highly-continuous basis functions…
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The…
Full-potential electronic structure calculations for periodic systems retain the Coulomb singularity at the nuclei, which induces cusp behavior of the orbitals near the nuclei while leaving the interstitial region smooth. This multiscale…
The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical…
To exploit the advantageous properties of isogeometric analysis (IGA) in a scan-based setting, it is important to extract a smooth geometric domain from the scan data (e.g., voxel data). IGA-suitable domains can be constructed by…
Implicit Neural Representations (INRs) that learn Signed Distance Functions (SDFs) from point cloud data represent the state-of-the-art for geometrically accurate 3D scene reconstruction. However, training these Neural SDFs often requires…