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Modal decomposition methods are important for characterizing the low-dimensional dynamics of complex systems, including turbulent flows. Different methods have varying data requirements and produce modes with different properties. Spectral…
We present a novel, physically-based morphing technique for elastic shapes, leveraging the differentiable material point method (MPM) with space-time control through per-particle deformation gradients to accommodate complex topology…
We develop a numerical code to calculate the neutrino transfer with multi-energy and multi-angle in three dimensions (3D) for the study of core-collapse supernovae. The numerical code solves the Boltzmann equations for neutrino…
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…
Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…
Multiple-input multiple-output (MIMO) systems play an essential role in direction-of-arrival (DOA) estimation. A large number of antennas used in a MIMO system imposes a huge complexity burden on the popular DOA estimation algorithms, such…
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…
We present a method of calculation of the effective magnetic permeability of magnonic metamaterials containing periodically arranged magnetic inclusions of arbitrary shapes. The spectrum of spin wave modes confined in the inclusions is…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
This work aims to provide standard formulations for direct minimization approaches on various types of static problems of continuum mechanics. Particularly, form-finding problems of tension structures are discussed in the first half and the…
There are several numerical models that describe real phenomena being used to solve complex problems. For example, an accurate numerical breast model can provide assistance to surgeons with visual information of the breast as a result of a…
We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data…
The dynamic structure factor and the eigenmodes of density fluctuations in the uniform liquid $^3$He are studied using a novel non-perturbative approach. This new version of the self-consistent method of moments invokes up to nine sum rules…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
In this work, we present a deep collocation method for three dimensional potential problems in nonhomogeneous media. This approach utilizes a physics informed neural network with material transfer learning reducing the solution of the…
We solve the wave equation with periodically time-modulated material parameters in a one-dimensional high-contrast resonator structure in the subwavelength regime exactly, for which we compute the subwavelength quasifrequencies numerically…
Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the…