相关论文: A two level method for isogeometric discretization…
Physics-informed neural networks (PINNs) formulate the solution of partial differential equations as residual minimization problems over neural network parameterizations. Although highly flexible, optimization of PINNs using modern variants…
A seamless integration of neural networks with Isogeometric Analysis (IGA) was first introduced in [1] under the name of Hierarchical Deep-learning Neural Network (HiDeNN) and has systematically evolved into Isogeometric Convolution HiDeNN…
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline…
We propose and analyze optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern and Peterseim (2015, Comput. Aided Geom.…
Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding local grid refinement and variation of polynomial degrees for a variety of different problem classes. With a focus on diffusion problems, we consider DG…
In this paper, we propose a $W$-cycle $p$-multigrid method for solving the $p$-version symmetric interior penalty discontinuous Galerkin (SIPDG) discretization of elliptic problems. This SIPDG discretization employs hierarchical Legendre…
In this contribution, we derive a consistent variational formulation for computational homogenization methods and show that traditional FE2 and IGA2 approaches are special discretization and solution techniques of this most general…
We propose a novel approach to the analysis of programmable geometrically exact shear deformable beam systems made of shape memory polymers. The proposed method combines the viscoelastic Generalized Maxwell model with the Williams, Landel…
In this paper, we propose an efficient two-level additive Schwarz method for solving large-scale eigenvalue problems arising from the finite element discretization of symmetric elliptic operators, which may compute efficiently more interior…
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…
In this paper, we study the multi-patch discontinuous Galerkin isogeometric (DG-IGA) approximations for full-potential electronic structure calculations. We decompose the physical domain into several subdomains, represent each part of the…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…
We consider the linearized elasticity equation, discretized with multi-patch Isogeometric Analysis. A standard discretization error analysis is based on Korn's inequality, which degrades for certain geometries, such as long and thin…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
In electronic structure calculations, various material properties can be obtained by means of computing the total energy of a system as well as derivatives of the total energy w.r.t. atomic positions. The derivatives, also known as…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g., provided by a Computer…
In this paper we consider a new version of the dual-primal isogeometric tearing and interconnecting (IETI-DP) method for solving large-scale linear systems of algebraic equations arising from discontinuous Galerkin (dG) isogeometric…
If we wish to integrate a function $h|\Omega\subset\Re^{n}\to\Re$ along a single $T$-level surface of a function $\psi |\Omega\subset\Re^{n}\to\Re$, then a number of different methods for extracting finite elements appropriate to the…