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Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC…
We report an ab initio evaluation of the surface energy of a simple metal, performed via a coupling-constant integration over the dynamical density-response function. The rapid rate of change of the electron density at the surface is…
We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…
3D equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two three-dimensional equilibrium codes, VMEC, which uses a…
We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…
We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the…
This paper presents a directional proximal point method (DPPM) to derive the minimum of any C1-smooth function f. The proposed method requires a function persistent a local convex segment along the descent direction at any non-critical…
We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by…
This paper presents a new methodology and algorithm for solving post buckling problems of a large deformed elastic beam. The total potential energy of this beam is a nonconvex functional, which can be used to model both pre- and…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order partial differential equations. By decoupling the primary PDE…
The one-dimensional PDE model of the wave equation with a state feedback controller at its boundary, which describes wave dynamics of a wide-range of controlled mechanical systems, has exponentially stable solutions. However, it is known…
Novel algorithm for designing values of technological parameters for production of Soft Magnetic Composites (SMC) has been created. These parameters are the following magnitudes: hardening temperature $T$ and compaction pressure $p$. They…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach…