We describe a GPUand multicore-oriented implementation technique for a key component of finite element based simulation toolkits for partial differential equations on unstructured grids: Geometric Multigrid solvers. We use efficient sparse matrix-vector multiplications throughout the solver pipeline: within the coarse-grid solver, smoothers and even grid transfers. Our implementation can handle...

This article presents a method for solving large-scale linear inverse imaging problems regularized with a nonlinear, edge-preserving penalty term such as total variation or the Perona–Malik technique. Our method is aimed at problems defined on unstructured meshes, where such regularizers naturally arise in unfactorized form as a stiffness matrix of an anisotropic diffusion operator and factoriz...

We present a highly parallel graph mapping technique that enables one to efficiently solve unstructured grid problems on massively parallel computers. Many implicit and explicit methods for solving discretized partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The time spent communicating can limit t...

We present an overview of SCIRun, a scientiic problem solving environment that allows the interactive construction, debugging, and steering of large-scale scientiic computations. Using this \computational work-bench," a scientist can design and modify simulations interactively via a dataaow programming model. SCIRun enables scientists to design and modify model geometry, interactively change si...

The e ciency of three multigrid methods for solving highly non-linear di usion problems on two-dimensional unstructured meshes is examined. The three multigrid methods di er mainly in the manner in which the non-linearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directl...

Organizations, especially those adapting to rapidly changing environments , face the challenge of being able to solve complex problems within highly constrained timeframes. Complex problem solving has been addressed by theories of bounded rationality. However, these theories focus on solving complex but structured problems, and thus, context and how it emerges and transforms is not a central is...

We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our allows generating circuits that use asymptotically fewer additional gates than famous Grover's and may be successfully executed on NISQ devices. prove our is optimal in total number of elementary up to multiplicative constant. As many NP-hard problems are not fact unstructured, we also ...

Many large scale computational problems are based on unstruc-tured computational domains. Primary examples are unstructured grid calculations based on finite volume methods in computational fluid dynamics, or structural analysis problems based on finite element approximations. Here we will address the question of how to distribute such unstructured computational domains over a large number of p...

In this chapter the method of lines is applied to computational models of reacting flow arising from atmospheric applications. These computational models describe the chemical transformations and transport of species in the troposphere and have an essential role in understanding the complex processes which lead to the formation of pollutants such as greenhouse gases, acid rain and photochemical...