Related papers: 3rd-order Spectral Representation Method: Part I -…
Neural implicit reconstruction via volume rendering has demonstrated its effectiveness in recovering dense 3D surfaces. However, it is non-trivial to simultaneously recover meticulous geometry and preserve smoothness across regions with…
We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
Inverse scattering involving microwave and ultrasound waves require numerical solution of nonlinear optimization problem. To alleviate the computational burden of a full three-dimensional (3-D) inverse problem, it is a common practice to…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…
Idier et al. [IEEE Trans. Comput. Imaging 4(1), 2018] propose a method which achieves superresolution in the microscopy setting by leveraging random speckle illumination and knowledge about statistical second order moments for the…
We develop a method for modeling and simulating a class of two-phase flows consisting of two immiscible incompressible dielectric fluids and their interactions with imposed external electric fields in two and three dimensions. We first…
The recent success of 3D Gaussian Splatting (3DGS) has reshaped novel view synthesis by enabling fast optimization and real-time rendering of high-quality radiance fields. However, it relies on simplified, order-dependent alpha blending and…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
Radiance fields have revolutionized photo-realistic 3D scene visualization by enabling high-fidelity reconstruction of complex environments, making them an ideal match for light field displays. However, integrating these technologies…
The probability density function of the random flight with isotropic initial conditions is obtained by an expansion in the number of collisions and the in the spatial harmonics of the solution, as in a Fourier series. The method holds for…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and optics design of nanostructured components. As has been shown in previous benchmarks some of the presently used…
Second-order structure functions and power spectral densities are popular tools in the study of statistical properties across scales, particularly for the analysis of turbulent flows. Although intimately related, analyses primarily use one…
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…
Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve…
Across many plasma applications, the underlying phenomena and interactions among the involved processes are known to exhibit three-dimensional characteristics. Furthermore, the global properties and evolution of plasma systems are often…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…