An inverse spectral problem for a damped wave operator

Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation

In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze a time stepping method for the numerical solution of the corresponding forward problem. Moreover, to efficiently obtain reconstructions by minimizing a Tikhonov regularization functional (or alternatively, by computing the MAP estimator in a Bayesian approach), we develop an adjoint based scheme for gradient computation. Numerical reconstructions in two spa…

A linearized and conservative Fourier pseudo-spectral method for the damped nonlinear Schrödinger equation in three dimensions

In this paper, we propose a linearized Fourier pseudo-spectral method, which preserves the total mass and energy conservation laws, for the damped nonlinear Schrödinger equation in three dimensions. With the aid of the semi-norm equivalence between the Fourier pseudo-spectral method and the finite difference method, an optimal $L^2$-error estimate for the proposed method without any restriction on the grid ratio is established by analyzing the real and imaginary parts of the error function. Numerical results are addressed to confirm our theoretical analysis.

通过一个遍历数值方案近似耗散随机非线性薛定谔方程的不变测度

Approximation of Invariant Measure for Damped Stochastic Nonlinear Schrödinger Equation via an Ergodic Numerical Scheme

本文提出一种全离散方案，结合谱伽辽金方法和隐式欧拉法的改进，证明数值解的唯一遍历性并给出不变测度的误差估计，空间方向为二阶，时间方向为半阶。

使用自适应参数化求解抛物型逆对流-扩散-反应问题

Parabolic inverse convection-diffusion-reaction problem solved using an adaptive parametrization

针对基于对流-扩散-反应方程的抛物型逆问题，分别采用投影阻尼高斯-牛顿法和自适应时间局部参数化方法处理已知和未知源位置的情况，并利用本征正交分解加速优化循环。

一类随机阻尼波动方程不变分布的数值逼近

Numerical approximation of the invariant distribution for a class of stochastic damped wave equations

本文研究加性维纳噪声驱动的随机半线性阻尼波动方程，利用谱伽辽金和指数欧拉方法离散化，证明数值格式具有唯一不变分布并给出误差估计，为首次相关数值逼近研究。

一种求解含聚焦非线性项的阻尼非线性薛定谔方程的显式无条件稳定数值方法

An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity

本文提出一种显式、无条件稳定的时间分裂正弦谱方法求解阻尼聚焦非线性薛定谔方程，数值实验表明三次或五次阻尼可阻止爆聚，线性阻尼需超过阈值，并可推广至三维BEC动力学模拟。