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In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…

Machine Learning · Computer Science 2023-03-10 Bian Li , Hanchen Wang , Shihang Feng , Xiu Yang , Youzuo Lin

Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high…

Numerical Analysis · Mathematics 2013-11-07 Barbara Kaltenbacher , Vanja Nikolic , Mechthild Thalhammer

This paper is concerned with the strong approximation of a semi-linear stochastic wave equation with strong damping, driven by additive noise. Based on a spatial discretization performed by a spectral Galerkin method, we introduce a kind of…

Numerical Analysis · Mathematics 2020-08-10 Ruisheng Qi , Xiaojie Wang

In this paper, a highly efficient fast boundary element method (BEM) for solving large-scale engineering acoustic problems in a broad frequency range is developed and implemented. The acoustic problems are modeled by the Burton-Miller…

Numerical Analysis · Computer Science 2015-11-16 Yanchuang Cao , Lihua Wen , Jinyou Xiao , Yijun Liu

Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…

Numerical Analysis · Mathematics 2025-03-21 Hao Yuan , Xiaoping Xie

We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the…

Numerical Analysis · Mathematics 2024-04-02 Simin Shekarpaz , Fanhai Zeng , George Karniadakis

This paper tackles the problem of real-time semantic segmentation of high definition videos using a hybrid GPU / CPU approach. We propose an Efficient Video Segmentation(EVS) pipeline that combines: (i) On the CPU, a very fast optical flow…

Computer Vision and Pattern Recognition · Computer Science 2019-12-30 Matthieu Paul , Christoph Mayer , Luc Van Gool , Radu Timofte

The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…

Numerical Analysis · Mathematics 2020-10-28 Zhengqi Zhang , Zhi Zhou

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Optimization and Control · Mathematics 2025-09-03 Mootta Prangprakhon , Nimit Nimana

The wavenumber integration model is considered to be the most accurate algorithm for arbitrary horizontally stratified media in computational ocean acoustics. In contrast to the normal mode approach, it considers not only the discrete…

Numerical Analysis · Mathematics 2023-05-25 Houwang Tu , Yongxian Wang , Wei Liu , Shuqing Ma , Xiaodong Wang

In this paper, we present a novel numerical scheme for simulating deformable and extensible capsules suspended in a Stokesian fluid. The main feature of our scheme is a partition-of-unity (POU) based representation of the surface that…

Numerical Analysis · Mathematics 2024-04-09 Dhwanit Agarwal , George Biros

In this paper, we present a robust and fully discretized method for solving the time fractional diffusion equation with high-contrast multiscale coefficients. We establish the homogenized equation using a multicontinuum approach and employ…

Numerical Analysis · Mathematics 2025-07-30 Yifei Gao , Yating Wang , Wing Tat Leung , Zhengya Yang

In this article, we introduce a new method which allows utilizing all the available sub-stencils of a WENO scheme to increase the accuracy of the numerical solution of conservation laws while preserving the non-oscillatory property of the…

Computational Physics · Physics 2024-10-15 Hossein Mahmoodi Darian

This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…

Numerical Analysis · Mathematics 2020-08-10 Xiaojie Wang

Mesoscopic numerical simulation has become an important tool in thermal management and energy harvesting at the micro/nano scale, where the Fourier's law failed. However, it is not easy to efficiently solve the phonon Boltzmann transport…

Computational Physics · Physics 2022-12-13 Chuang Zhang , Samuel Huberman , Xinliang Song , Jin Zhao , Songze Chen , Lei Wu

This work is dedicated to the development and comparison of WENO-type reconstructions for hyperbolic systems of balance laws. We are particularly interested in high order shock capturing non-oscillatory schemes with uniform accuracy within…

Numerical Analysis · Mathematics 2018-07-09 Isabella Cravero , Gabriella Puppo , Matteo Semplice , Giuseppe Visconti

In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…

The numerical simulation of weakly nonlinear ultrasound is important in treatment planning for focused ultrasound (FUS) therapies. However, the large domain sizes and generation of higher harmonics at the focus make these problems extremely…

We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…

Numerical Analysis · Mathematics 2024-11-12 Shubin Fu , Eric Chung , Guanglian Li

In this work, we construct a fifth-order weighted essentially non-oscillatory (WENO) scheme with exponential approximation space for solving dispersive equations. A conservative third-order derivative formulation is developed directly using…

Numerical Analysis · Mathematics 2024-05-13 Lavanya V Salian , Samala Rathan