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In this paper, we propose a multiscale method for the Darcy-Forchheimer model in highly heterogeneous porous media. The problem is solved in the framework of generalized multiscale finite element methods (GMsFEM) combined with a multipoint…
The multi-layer multi-configuration time-dependent Hartree method (ML-MCTDH) is a highly efficient scheme for studying the dynamics of high-dimensional quantum systems. Its use is greatly facilitated if the Hamiltonian of the system…
The Complex Kohn variational method for electron-polyatomic molecule scattering is formulated using an overset grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense,…
We develop a full-wave electromagnetic (EM) theory for calculating the multipole decomposition in two-dimensional (2-D) structures consisting of isolated, arbitrarily shaped, inhomogeneous, anisotropic cylinders or a collection of such. To…
We develop and implement a new mathematical and computational framework for designing photonic elements with one or more high-$Q$ scattering resonances. The approach relies on solving for the poles of the scattering matrix, which…
Theoretical material investigation based on density functional theory (DFT) has been a breakthrough in the last century. Nevertheless, the optical properties calculated by DFT generally show poor agreement with experimental results…
Multisequence Magnetic Resonance Imaging (MRI) provides a more reliable diagnosis in clinical applications through complementary information across sequences. However, in practice, the absence of certain MR sequences is a common problem…
In [Phys. Rev. Lett. 128, 013001 (2022)] a novel ground state method was proposed. It has been suggested that this $i$-DMFT would be a method within one-particle reduced density matrix functional theory (DMFT), capable of describing…
We present a charge and self-energy self-consistent computational scheme for correlated systems based on the Korringa-Kohn-Rostoker (KKR) multiple scattering theory with the many-body effects described by the means of dynamical mean field…
In this work, we propose a structured illumination (SI) method based on a two-photon excitation (TPE) scanning laser beam. Advantages of TPE methods include optical sectioning, low photo-toxicity, and robustness in the face of sample…
The advances in fabrication processes in different material platforms employed in integrated optics are opening the path towards the implementation of circuits with increasing degree of complexity. In addition to the more conventional…
Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised…
The Point Spread Function (PSF) is a key figure of merit for specifying the angular resolution of optical systems and, as the demand for higher and higher angular resolution increases, the problem of surface finishing must be taken…
This paper is concerned with efficient representations and approximations of the solution to the scattering problem by a system of strongly coupled plasmonic particles. Three schemes are developed: the first is the resonant expansion which…
We present the pupil phase series (PPS), a fast and accurate forward scattering algorithm for simulating and inverting multiple light scattering in large biological samples. PPS achieves high-angle scattering accuracy and energy…
This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
In this paper, we review the main problem concerning the calculation of X-ray scattering of simulated model systems, namely their finite size. A novel method based on the Rayleigh-Debye-Gans approximation was derived, which allows…
Multiple importance sampling (MIS) is an indispensable tool in rendering that constructs robust sampling strategies by combining the respective strengths of individual distributions. Its efficiency can be greatly improved by carefully…
This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and…