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...
Efficient numerical approximation of a non-regular Fokker-Planck equation associated with first-passage time distributions [0.03%]
与首次通过时间分布相关的非正则Fokker-Planck方程的有效数值逼近
Udo Boehm,Sonja Cox,Gregor Gantner et al.
Udo Boehm et al.
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker-Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation is...
Computable upper error bounds for Krylov approximations to matrix exponentials and associated [Formula: see text] -functions [0.03%]
Krylov矩阵指数和相关函数的可计算上界误差估计式
Tobias Jawecki,Winfried Auzinger,Othmar Koch
Tobias Jawecki
An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approximation and is proven to constitute a rigorous upper bound on...