Related papers: Characterizing nonconvex boundaries via scalarizat…
The purpose of this paper is three-fold. Firstly we attack a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions. The investigated problem involves a nonlinear monotone partial differential…
We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…
In this work we consider topology optimization of systems, which are governed by the external Bernoulli free boundary problem. We utilize the so-called pseudo-solid approach to solve the governing free boundary problems during the…
Pseudoconvexity of a domain in $\Bbb C^n$ is described in terms of the existence of a locally defined plurisubharmonic/holomorphic function near any boundary point that is unbounded at the point.
We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized…
This article surveys recent results aiming at obtaining refined mapping estimates for the X-ray transform on a Riemannian manifold with boundary, which leverage the condition that the boundary be strictly geodesically convex. These…
For the first time, a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions is analyzed. The investigated problem involves a nonlinear monotone partial differential equation in the interior…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
We propose an exact algorithm for solving biobjective integer programming problems, which arise in various applications of operations research. The algorithm is based on solving Pascoletti-Serafini scalarizations to search specified regions…
A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…
The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…
This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational…
We present two algorithms for large-scale low-rank Euclidean distance matrix completion problems, based on semidefinite optimization. Our first method works by relating cliques in the graph of the known distances to faces of the positive…
Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…
We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function $P$ and integral identities. In dimension…
Most genuine multi-sided surface representations depend on a 2D domain that enables a mapping between local parameters and global coordinates. The shape of this domain ranges from regular polygons to curved configurations, but the simple…
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. This is applied by Du (2010) [A note on cone…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…