Visualization of CFD simulation data on unstructured, 3D grids poses several challenges. The wide range of real-world data set sizes and the geometric versatility within individual, unstructured CFD simulation models present special challenges to the engineers analyzing flow simulation results. Users also face perceptual problems such as occlusion, visual complexity, lack of directional cues, a...

This paper investigates how readily an unsolvable constraint satisfaction problem can be reformulated so that it becomes solvable. We investigate small changes in the definitions of the problem’s constraints, changes that alter neither the structure of its constraint graph nor the tightness of its constraints. Our results show that structured and unstructured problems respond differently to suc...

This computational paper presents a method to solve k-cluster problems exactly by intersecting semidefinite and polyhedral relaxations. Our algorithm uses a generic branch-and-bound method featuring an improved semidefinite bounding procedure. Extensive numerical experiments show that this algorithm outperforms the best known methods both in time and ability to solve large instances. For the fi...

Peer-to-peer systems have largely replaced the client-server architecture. There are different solutions for the arising problems of efficient object location, scalability, and robustness, resulting in different approaches. We give a short overview of the concepts of structured and unstructured peer-to-peer networks and discuss the handling of those problems in each case. In particular, the Bit...

Skew-Hamiltonian and Hamiltonian eigenvalue problems arise from a number of applications, particularly in systems and control theory. The preservation of the underlying matrix structures often plays an important role in these applications and may lead to more accurate and more efficient computational methods. We will discuss the relation of structured and unstructured condition numbers for thes...

In this paper we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods in complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficien...

This paper presents a method to solve k-cluster problems by intersecting semidefinite and polyhedral relaxations. We use a generic branch-and-bound method featuring an improved semidefinite bounding procedure. Extensive numerical experiments show that our algorithm outperforms the best known methods in both time and ability to solve large instances. For the first time, numerical results are rep...

We propose a linear finite-element discretization of Dirichlet problems for static Hamilton–Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the...

Explicit time-stepping methods are commonly used to solve transient, timedependent problems. For problems involving small-scale features, adaptive unstructured mesh refinement can be effective. Unfortunately, using such dynamic strategies on parallel computers can result in difficult load balancing issues because of the relatively high cost of the mesh partitioning to the time-step computation....

We discuss optimal control problems for general unstructured linear differentialalgebraic equations of arbitrary index. We discuss controllability and observability in the higher order case and show that order reduction may lead to false results. We then derive necessary conditions in the case of linear-quadratic control problems and show how these lead to eigenvalue problems for for even matri...