Search Results

We present a non-iterative Schur complement method for the solution of a fluid-structure interaction problem, employing projection-based reduced order models (ROMs) on one or both subdomains. The formulation is strongly coupled, using a Lagrange ...

• Extends a non-iterative Schur complement method for fluid-structure interaction.
• Couples a projection-based reduced order model with a reduced or full order model.
• Utilizes supremizer enrichment for velocity and displacement.
• ...

We develop two unfitted finite element methods for the Stokes equations based on ${\mathbf{H}}^{\text{div}}$-conforming finite elements. Both cut finite element methods exhibit optimal convergence order for the velocity, pointwise divergence-free velocity fields, and ...${\mathbf{}}^{}$

We look at computational physics from an electrical engineering perspective and suggest that several concepts of mathematics, not so well-established in computational physics literature, present themselves as opportunities in the field. We discuss ...

We propose two implicit numerical schemes for the low-rank time integration of stiff nonlinear partial differential equations. Our approach uses the preconditioned Riemannian trust-region method of Absil, Baker, and Gallivan, 2007. We demonstrate ...

Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H ( grad curl )-nonconforming but H ( curl )-conforming finite elements are constructed, which are extended to nonconforming finite ...

A randomized algorithm for computing a data sparse representation of a given rank-structured matrix A (a.k.a. an H-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the assumption ...

The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two-dimensional domain. The scheme decomposes the domain into thin subdomains, or “slabs” and uses a two-level approach ...${\mathcal{}}^{\mathbf{}}$$\mathcal{}$${\mathcal{}}^{\mathbf{}}$${\mathcal{}}^{\mathbf{}}$$\mathbf{}\mathit{}\mathbf{}\mathit{}$$\mathit{}\mathbf{}\mathbf{}$

In exterior calculus on smooth manifolds, the exterior derivative and wedge products are natural with respect to smooth maps between manifolds, that is, these operations commute with pullback. In discrete exterior calculus (DEC), simplicial ...

• Detailed modeling of the Saint-Venant torsion problem for heterogeneous and orthotropic cross-sections.
• Rigorous analy sis of well-posedness, regularity and Galerkin convergence of solutions for different continuous variational ...

For many years, torsion of arbitrary cross-sections has been a subject of numerous investigations from theoretical and numerical points of view. As it is well known, the resulting boundary value problem (BVP) governing such phenomenon happens to ...

Many neurodegenerative diseases are connected to the spreading of misfolded prionic proteins. In this paper, we analyse the process of misfolding and spreading of both $\alpha$-synuclein and Amyloid-$\beta$, related to Parkinson’s and Alzheimer’s diseases, ...$$$$$$

This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of predefining ...

We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local $H^1$ error in a interior subdomain is bounded by a term behaving ...

In this paper, we present a novel second-order generalised rotational discrete gradient scheme for numerically approximating the orthonormal frame gradient flow of biaxial nematic liquid crystals. This scheme relies on reformulating the original ...

Efficient and robust iterative solvers for strongly anisotropic elliptic equations are very challenging. Indeed, the discretization of this class of problems gives rise to a linear system with a condition number increasing with anisotropic ...$\mathrm{}\mathrm{}$

We introduce a new discretization based on a polynomial Trefftz-DG method for solving the Stokes equations. Discrete solutions of this method fulfill the Stokes equations pointwise within each element and yield element-wise divergence-free ...

New low-order $H(\text{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order normal-normal face ...${\mathrm{}}^{\mathrm{}}$$$

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information about the target PDEs such as its ...

In this paper, we investigate a low-order robust numerical method for the linear elasticity problem. The method is based on a Bernardi–Raugel-like $\mathit{H}(\text{div})$-conforming method proposed first for the Stokes flows in [Li and Rui, IMA J. Numer. Anal. 42 (...$\mathit{}$${\mathit{}}_{\mathrm{}}$${\mathit{}}_{\mathrm{}}{}_{\mathrm{}}$${\mathit{}}_{\mathrm{}}{\mathit{}}_{\mathrm{}}{}_{\mathrm{}}$$$${\mathit{}}^{\mathrm{}}$$\mathcal{}{}^{\mathrm{}}$${\mathit{}}_{\mathrm{}}{\mathit{}}_{\mathrm{}}$${\mathit{}}_{\mathrm{}}$${\mathit{}}^{\mathrm{}}$

In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω ⊂ R d, d ≥ 1. When Ω = [ 0 , 1 ], such graphs include the standard Toeplitz graphs and, for Ω = [ 0 , 1 ] d,...

We formulate and analyze a fully discrete approximate solution of the linear Schrödinger equation on the unit square written as a Schrödinger-type system. The finite element Galerkin method is used for the spatial discretization, and the time ...${}^{\mathrm{}}{}^{\mathrm{}}$${}^{}$