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Crack nucleation is crucial in many industrial applications. The phase field method for fracture transforms the crack nucleation problem into a minimization problem of the sum of the elastic potential energy and the crack surface energy.…
Newton's Method is widely used to find the solution of complex non-linear simulation problems in Computer Graphics. To guarantee a descent direction, it is common practice to clamp the negative eigenvalues of each element Hessian prior to…
A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…
Dust-gas mixtures are the simplest example of a two fluid mixture. We show that when simulating such mixtures with particles or with particles coupled to grids a problem arises due to the need to resolve a very small length scale when the…
This paper is on the construction of structure-preserving, online-efficient reduced models for the barotropic Euler equations with a friction term on networks. The nonlinear flow problem finds broad application in the context of gas…
A technique for accelerating global convergence of pseudo-transient continuation Newton methods is proposed based on residual smoothing. The technique is motivated by the effectiveness of local nonlinear smoothers at overcoming strong…
The self-gravitating gas in thermal equilibrium is studied using a Newtonian potential regularized at short distances. This short distance cutoff permits us to obtain a complete description of the gas including its collapsed phase. We give…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite…
The Gauss-Newton's method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local…
The adjoint equation was introduced in the early days of neutron transport and its solution, the neutron importance, has ben used for several applications in neutronics. The work presents at first a critical review of the adjoint neutron…
In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
Three different methods viz. i) a perturbative analysis of the Schr\"odinger equation ii) abstract differential geometric method and iii) a semiclassical reduction of the Wheeler-Dewitt equation, relating Pancharatnam phase to vacuum…
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations…
In this paper we generalize the technique of deflation to define two new methods to systematically find many local minima of a nonlinear least squares problem. The methods are based on the Gauss-Newton algorithm, and as such do not require…
In this paper, we consider variants of Newton-MR algorithm for solving unconstrained, smooth, but non-convex optimization problems. Unlike the overwhelming majority of Newton-type methods, which rely on conjugate gradient algorithm as the…
The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear…
Gas transportation and storage has become one of the most relevant and important optimization problems in energy systems. This problem inherently includes highly nonlinear and nonconvex aspects due to gas physics, and discrete aspects due…