Application of randomized quadrature formulas to the finite element method for elliptic equations [0.03%]
随机积分公式在椭圆型方程有限元方法中的应用
Raphael Kruse,Nick Polydorides,Yue Wu
Raphael Kruse
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be approx...
Optimal error estimates of the diffuse domain method for second order parabolic equations [0.03%]
关于抛物方程扩散域方法的最优误差估计
Wenrui Hao,Lili Ju,Yuejin Xu
Wenrui Hao
In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann boundary condition posed on general irregular domains. The DDM emp...
An accelerated Levin-Clenshaw-Curtis method for the evaluation of highly oscillatory integrals [0.03%]
一种求解强振荡积分的加速Levin-Clenshaw-Curtis方法
Arieh Iserles,Georg Maierhofer
Arieh Iserles
The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive in the high-frequency regime, Levin methods provide a way to ...
Conservation properties of non-conforming embedded finite-element methods based on lagrange multipliers [0.03%]
基于拉格朗日乘子的非协调嵌入式有限元方法的保真性质研究
Maria Giuseppina Chiara Nestola,Patrick Zulian,Marco Favino et al.
Maria Giuseppina Chiara Nestola et al.
Numerical simulations of Darcy flow in fractured porous media rely on hybrid- or equi-dimensional fracture models. The former considers fractures as lower-dimensional manifolds, while the latter treats them as objects of the same geometrica...
Super-localized orthogonal decomposition for convection-dominated diffusion problems [0.03%]
对主导扩散问题的超局部正交分解
Francesca Bonizzoni,Philip Freese,Daniel Peterseim
Francesca Bonizzoni
This paper presents a novel multi-scale method for convection-dominated diffusion problems in the regime of large Péclet numbers. The method involves applying the solution operator to piecewise constant right-hand sides on an arbitrary coa...
Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift [0.03%]
跳移扩散型SDE的误差下界与最优逼近性（当漂移不连续时）
Paweł Przybyłowicz,Verena Schwarz,Michaela Szölgyenyi
Paweł Przybyłowicz
In this paper sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift are proven. The approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted...
Block diagonal Calderón preconditioning for scattering at multi-screens [0.03%]
散频于多屏散射的分块对角Calderon预处理
Kristof Cools,Carolina Urzúa-Torres
Kristof Cools
A preconditioner is proposed for Laplace exterior boundary value problems on multi-screens. To achieve this, the quotient-space boundary element method and operator preconditioning are combined. For a fairly general subclass of multi-screen...
Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils [0.03%]
一类随机化数值方法的特征值条件数分析（奇异矩阵铅笔）
Daniel Kressner,Bor Plestenjak
Daniel Kressner
The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the ...
From low-rank retractions to dynamical low-rank approximation and back [0.03%]
从低秩流形的递缩映射到动态低秩近似及其逆问题
Axel Séguin,Gianluca Ceruti,Daniel Kressner
Axel Séguin
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a usefu...
Benjamin Carrel,Martin J Gander,Bart Vandereycken
Benjamin Carrel
In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used as time stepper. Many discrete integrators for DLRA have rec...