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The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations…
Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier…
In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
Accurate channel estimation is essential for achieving the performance gains offered by reconfigurable intelligent surface (RIS)-aided wireless communications. A variety of channel estimation methods have been proposed for such systems;…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…
Accurate quantum mechanical treatment of molecular reactions remains a longstanding challenge, especially for reactions involving deep potential wells and long-lived intermediate complexes. Here, we introduce an interaction region…
In this work, we develop a class of high-order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recently developed Hermite-Birkhoff-Predictor-Corrector methods…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
Specific emitter identification (SEI) utilizes passive hardware characteristics to authenticate transmitters, providing a robust physical-layer security solution. However, most deep-learning-based methods rely on extensive data or require…
The Proportional-Integral-Derivative Controller is widely used in industries for process control applications. Fractional-order PID controllers are known to outperform their integer-order counterparts. In this paper, we propose a new…
This paper presents a novel semi-analytical collocation method to solve multi-term variable-order time fractional partial differential equations (VOTFPDEs). In the proposed method it employs the Fourier series expansion for spatial…
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…
Full waveform inversion (FWI) is an iterative identification process that serves to minimize the misfit of model-based simulated and experimentally measured wave field data, with the goal of identifying a field of parameters for a given…
In this paper, a non-intrusive reduced-order model (ROM) for parametric reactor kinetics simulations is presented. Time-dependent ROMs are notoriously data intensive and difficult to implement when nonlinear multiphysics phenomena are…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
Recently, compositional optimization (CO) has gained popularity because of its applications in distributionally robust optimization (DRO) and many other machine learning problems. Large-scale and distributed availability of data demands the…
This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…
This paper proposes an anti-interference affine frequency division multiplexing (AFDM) system to ensure reliability and resource efficiency under malicious high-power interference originating from adversarial devices in high-mobility…