arXiv subjects

Jinrui Zhang

Publications and source records attributed to Jinrui Zhang.

40 records · Page 3Linked to original sources

arXiv2023

Singularity swapping method for nearly singular integrals based on trapezoidal rule

Accurate evaluation of nearly singular integrals plays an important role in many boundary integral equation based numerical methods. In this paper, we propose a variant of singularity swapping method to accurately evaluate the layer potentials for arbitrarily close targets. Our method is based on the global trapezoidal rule and trigonometric interpolation, resulting in an explicit quadrature formula. The method achieves spectral accuracy for nearly singular integrals on closed analytic curves. In order to extract the singularity from the complexified distance function, an efficient root finding method is proposed based on contour integration. Through the change of variables, we also extend the quadrature method to integrals on the piecewise analytic curves. Numerical examples for Laplace's and Helmholtz equations show that high order accuracy can be achieved for arbitrarily close field evaluation.

math.NA↗

arXiv2023

Selective focusing of elastic cavities based on the time reversal far field model

This paper is concerned with the inverse time harmonic elastic scattering of multiple small and well-resolved cavities in two dimensions. We extend the so-called DORT method to the inverse elastic scattering so that selective focusing can be achieved on each cavity with far field measurements. A rigorous mathematical justification that relates the corresponding eigenfunctions of the time reversal operator to the locations of cavities is presented based on the asymptotic analysis of the far field operator and decaying property of oscillatory integrals. We show that in the regime $a\ll k^{-1}\ll L$, where $a$ denotes the size of cavity, $k$ is the compressional wavenumber $\kp$ or shear wavenumber $\ks$, and $L$ is the minimal distance between the cavities, each cavity gives rise to five significant eigenvalues and the corresponding eigenfunction generates an incident wave focusing selectively on that cavity. Numerical experiments are given to verify the theoretical result.

math.NA↗

arXiv2022

Exploiting Context Information for Generic Event Boundary Captioning

Generic Event Boundary Captioning (GEBC) aims to generate three sentences describing the status change for a given time boundary. Previous methods only process the information of a single boundary at a time, which lacks utilization of video context information. To tackle this issue, we design a model that directly takes the whole video as input and generates captions for all boundaries parallelly. The model could learn the context information for each time boundary by modeling the boundary-boundary interactions. Experiments demonstrate the effectiveness of context information. The proposed method achieved a 72.84 score on the test set, and we reached the $2^{nd}$ place in this challenge. Our code is available at: \url{https://github.com/zjr2000/Context-GEBC}

cs.CV↗

arXiv2022

Fast inverse elastic scattering of multiple particles in three dimensions

Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three dimensions. We measure the far field information and apply the time reversal method to recover the unknown elastic particles. Two regimes are considered depending on the size and distance among particles. First, an asymptotic analysis for the imaging of small and distant particles is given based on the scattering property of a single particle, which can be used for selective focusing. Second, when particles are not small but well-separated, a fast algorithm, based on the combination of multiple scattering theory and fast multipole method, is proposed to efficiently simulate the forward multiple scattering problem and applied in the inverse elastic scattering. Numerical experiments demonstrate the proposed method can determine the locations and shapes of multiple particles instantly.

math-ph↗