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The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for minimax problems, which we call $J$-symmetric quasi-Newton method.…
Partial Differential Equation (PDE)-constrained optimization problems often take the form of an optimization of an objective function given as a sum of loss terms. Each function or gradient evaluation requires one or more PDE solves, which…
Quasi-periodic trajectories with two or more incommensurate frequencies are ubiquitous in nonlinear dynamics, yet the classical Fourier-based time-spectral method is tied to strictly periodic responses. We introduce a torus time-spectral…
The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative…
Probing correlated states of many-body systems is one of the central tasks for quantum simulators and processors. A promising approach to state preparation is to realize desired correlated states as steady states of engineered dissipative…
We present a computational method for open-loop minimum-norm control synthesis for fixed-endpoint transfer of bilinear ensemble systems that are indexed by two continuously varying parameters. We suppose that one ensemble parameter scales…
In this paper, we introduce a novel parallel contact algorithm designed to run efficiently in High-Performance Computing based supercomputers. Particular emphasis is put on its computational implementation in a multiphysics finite element…
This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
Designing efficient quasi-Newton methods is an important problem in nonlinear optimization and the solution of systems of nonlinear equations. From the perspective of the matrix approximation process, this paper presents a unified framework…
In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into…
Integration of multimodal information from various sources has been shown to boost the performance of machine learning models and thus has received increased attention in recent years. Often such models use deep modality-specific networks…
In this study we present a non-overlapping Schwarz waveform relaxation (SWR) method applied to a one dimensional model problem representative of the coupling between the ocean and the atmosphere. This problem includes nonlinear interface…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such…
We propose a method to assist fault mitigation in quantum computation through the use of sensors co-located near physical qubits. Specifically, we consider using transition edge sensors co-located on silicon substrates hosting…
In this paper, the use of partitioned linear multistep methods (PLMM) as time integrators for the numerical approximation of some partial differential equations (pdes) is studied. We consider the periodic initial-value problem of two…
We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem…