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9 papers · 1 filter
A plane wave method based on approximate wave directions for two dimensional Helmholtz equations with large wave numbers
Qiya Hu, Zezhong Wang
In this paper we present and analyse a high accuracy method for computing wave directions defined in the geometrical optics ansatz of Helmholtz equation with variable wave number.…
Large deviations principles of sample paths and invariant measures of numerical methods for parabolic SPDEs
Chuchu Chen, Ziheng Chen, Jialin Hong +1
For parabolic stochastic partial differential equations (SPDEs), we show that the numerical methods, including the spatial spectral Galerkin method and further the full discretizat…
Optimal design for kernel interpolation: applications to uncertainty quantification
Akil Narayan, Liang Yan, Tao Zhou
The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation us…
An acceleration strategy for randomize-then-optimize sampling via deep neural networks
Liang Yan, Tao Zhou
Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO may be computationally intensive for complexity pr…
Large-stepsize integrators for charged-particle dynamics over multiple time scales
Ernst Hairer, Christian Lubich, Yanyan Shi
The Boris algorithm, a closely related variational integrator and a newly proposed filtered variational integrator are studied when they are used to numerically integrate the equat…
A variational analysis for the moving finite element method for gradient flows
Xianmin Xu
By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized p…