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A numerical scheme that uses multi-frequency Newton iterations to reconstruct a rough surface profile between two dielectric media is proposed. At each frequency sample, the scheme employs Newton iterations to solve the nonlinear inverse…
A method is developed for solving quasilinear convection diffusion problems starting on a coarse mesh where the data and solution-dependent coefficients are unresolved, the problem is unstable and approximation properties do not hold. The…
The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…
We propose Newton-PIPG, an efficient method for solving quadratic programming (QP) problems arising in optimal control, subject to additional set constraints. Newton-PIPG integrates the Proportional-Integral Projected Gradient (PIPG) method…
Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate…
This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…
Small-scale plasticity problems are often characterised by different patterning behaviours ranging from macroscopic down to the atomistic scale. In successful models of such complex behaviour, its origin lies within non-convexity of the…
In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a…
The coupled simulations of dynamic interactions between the well, hydraulic fractures and reservoir have significant importance in some areas of petroleum reservoir engineering. Several approaches to the problem of coupling between the…
Raylaigh-Benard convection is one of the most well-studied models in fluid mechanics. Atmospheric convection, one of the most important components of the climate system, is by comparison complicated and poorly understood. A key attribute of…
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…
A Bayesian multiple change-point model is proposed to analyse violations of air quality standards by pollutants such as nitrogen oxides (NO2 and NO) and carbon monoxide (CO). The model is built on the assumption that the occurrence of…
Urbanization has underscored the importance of understanding the pedestrian wind environment in urban and architectural design contexts. Pedestrian Wind Comfort (PWC) focuses on the effects of wind on the safety and comfort of pedestrians…
This article presents an innovative approach for developing an efficient reduced-order model to study the dispersion of urban air pollutants. The need for real-time air quality monitoring has become increasingly important, given the rise in…
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…
Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems. For instance, increased greenhouse gas concentrations are predicted to lead to drastic decreases in low…
A long-standing and formidable challenge faced by all conservative schemes for relativistic magnetohydrodynamics (RMHD) is the recovery of primitive variables from conservative ones. This process involves solving highly nonlinear equations…
This work links optimization approaches from hierarchical least-squares programming to instantaneous prioritized whole-body robot control. Concretely, we formulate the hierarchical Newton's method which solves prioritized non-linear…