Related papers: Extending fields in a level set method by solving …

The defect of valued field extensions is a major obstacle in open problems in resolution of singularities and in the model theory of valued fields, whenever positive characteristic is involved. We continue the detailed study of defect…

During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of…

This paper introduces an extension of the Morley element for approximating solutions to biharmonic equations. Traditionally limited to piecewise quadratic polynomials on triangular elements, the extension leverages weak Galerkin finite…

As one of the most popular interface-capturing methods, the level-set method is inherently non-conservative, and its evolution usually leads to unphysical mass gain/loss. In this paper, a novel conservative level set method is developed for…

This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…

We study the complexity of multiplication of two elements in a finite field extension given by their coordinates in a normal basis. We show how to control this complexity using the arithmetic and geometry of algebraic curves.

Stochastic physical problems governed by nonlinear conservation laws are challenging due to solution discontinuities in stochastic and physical space. In this paper, we present a level set method to track discontinuities in stochastic space…

In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…

This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…

The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…

This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function {\phi}ij represents the boundary between materials i and j.…

In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver…

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In…

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…

This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…

In this paper, we present and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then present a specific version of Cramer's rule…

A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…

We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadrature for the phase field function and hence is very easy to…

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…