Related papers: Combining plane wave expansion and variational tec…

Ultrafast ultrasound imaging is essential for advanced ultrasound imaging techniques such as ultrasound localization microscopy (ULM) and functional ultrasound (fUS). Current ultrafast ultrasound imaging is challenged by the ultrahigh data…

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…

This paper proposes a new source model and training scheme to improve the accuracy and speed of the multichannel variational autoencoder (MVAE) method. The MVAE method is a recently proposed powerful multichannel source separation method.…

In this paper, we systematically review a series of effective methods for studying the qualitative properties of solutions to fractional equations. Beginning with the pioneering extension method and the method of moving planes in integral…

A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach…

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…

Incommensurate heterostructures of two-dimensional (2D) materials, despite their attractive electronic behaviour, are challenging to simulate because of the absence of translation symmetry. Experimental investigations of these structures…

This work focuses on the study of partial differential equation (PDE) based basis function for Discontinuous Galerkin methods to solve numerically wave-related boundary value problems with variable coefficients. To tackle problems with…

This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in…

The weighted ensemble (WE) method, an enhanced sampling approach based on periodically replicating and pruning trajectories in a set of parallel simulations, has grown increasingly popular for computational biochemistry problems, due in…

A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation…

In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…

The present study addresses the question of total internal reflection of a plane wave from an amplifying or attenuating medium. Inspection on the expressions for the modal gain or loss of an asymmetric planar waveguide having an amplifying…

In [1], we introduced a new, matrix algebraic, performance analysis framework for wireless systems with fading channels based on the matrix exponential distribution. The main idea was to use the compact, powerful, and easy-to-use, matrix…

Sensor fusion can significantly improve the performance of many computer vision tasks. However, traditional fusion approaches are either not data-driven and cannot exploit prior knowledge nor find regularities in a given dataset or they are…

The two-dimensional discrete wavelet transform has a huge number of applications in image-processing techniques. Until now, several papers compared the performance of such transform on graphics processing units (GPUs). However, all of them…

In this paper we develop a plane wave type method for discretization of homogeneous Helmholtz equations with variable wave numbers. In the proposed method, local basis functions (on each element) are constructed by the geometric optics…

The variational discrete element method developed in [28] for dynamic elasto-plastic computations is adapted to compute the deformation of elastic Cosserat materials. In addition to cellwise displacement degrees of freedom (dofs), cellwise…

Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…

We present the pseudo-particle multipole method (P2M2), a new method to handle multipole expansion in fast multipole method and treecode. This method uses a small number of pseudo-particles to express multipole expansion. With this method,…