Related papers: C1 Triangular Isogeometric Analysis of the von Kar…
Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure $p$, the spatial part $\underline{u} \in \R^3$ of the dimensionless four-velocity and the particle density $n$. Radially symmetric solutions of…
Spline functions are smooth piecewise polynomials widely used for interpolation and smoothing, and nonnegative spline smoothing is also studied for nonnegative data. Previous research used sufficient conditions for the nonnegativity of…
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…
Satisfying spin-assignments in triangulations of a surface are states of minimum energy of the antiferromagnetic Ising model on triangulations which correspond (via geometric duality) to perfect matchings in cubic bridgeless graphs. In this…
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…
A geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements, and is suitable for both solid and liquid membranes. The curvilinear coordinate system is used to describe…
We propose a scalable approximate algorithm for the NP-hard maximum-weight independent set problem. The core component of our algorithm is a dual coordinate descent applied to a smoothed LP relaxation of the problem. This technique is…
We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries…
The objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3D configurations involving arbitrary beam-to-beam orientations. It is shown in a…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong…
An efficient method is presented for solving axisymmetric, frictionless contact problems between a rigid punch and an elastically non-homogeneous, power-law graded half-space. Provided that the contact area is simply-connected profiles of…