198,647 research outputs found
Immersed Boundary Smooth Extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods
The Immersed Boundary method is a simple, efficient, and robust numerical
scheme for solving PDE in general domains, yet it only achieves first-order
spatial accuracy near embedded boundaries. In this paper, we introduce a new
high-order numerical method which we call the Immersed Boundary Smooth
Extension (IBSE) method. The IBSE method achieves high-order accuracy by
smoothly extending the unknown solution of the PDE from a given smooth domain
to a larger computational domain, enabling the use of simple Cartesian-grid
discretizations (e.g. Fourier spectral methods). The method preserves much of
the flexibility and robustness of the original IB method. In particular, it
requires minimal geometric information to describe the boundary and relies only
on convolution with regularized delta-functions to communicate information
between the computational grid and the boundary. We present a fast algorithm
for solving elliptic equations, which forms the basis for simple, high-order
implicit-time methods for parabolic PDE and implicit-explicit methods for
related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat,
Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise
convergence for Dirichlet problems and third-order pointwise convergence for
Neumann problems
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Enterprise application reuse: Semantic discovery of business grid services
Web services have emerged as a prominent paradigm for the development of distributed software systems as they provide the potential for software to be modularized in a way that functionality can be described, discovered and deployed in a platform independent manner over a network (e.g., intranets, extranets and the Internet). This paper examines an extension of this paradigm to encompass ‘Grid Services’, which enables software capabilities to be recast with an operational focus and support a heterogeneous mix of business software and data, termed a Business Grid - "the grid of semantic services". The current industrial representation of services is predominantly syntactic however, lacking the fundamental semantic underpinnings required to fulfill the goals of any semantically-oriented Grid. Consequently, the use of semantic technology in support of business software heterogeneity is investigated as a likely tool to support a diverse and distributed software inventory and user. Service discovery architecture is therefore developed that is (a) distributed in form, (2) supports distributed service knowledge and (3) automatically extends service knowledge (as greater descriptive precision is inferred from the operating application system). This discovery engine is used to execute several real-word scenarios in order to develop and test a framework for engineering such grid service knowledge. The examples presented comprise software components taken from a group of Investment Banking systems. Resulting from the research is a framework for engineering servic
A local grid refinement technique based upon Richardson extrapolation
A grid-embedding technique for the solution of two-dimensional incompressible flows governed by the Navier-Stokes equations is presented. A single coarse grid covers the whole domain, and local grid refinement B carried out in the regions of high gradients without changing the basic grid structure. A finite volume method with collocated primitive variables is employed, ensuring conservation at the interfaces of embedded grids, as well as global conservation. The method is applied to the simulation of a turbulent flow past a backward facing step, the flow over a square obstacle, and the flow in a sudden pipe expansion, and the predictions are compared with data published in the literature. They show that neither the convergence rate nor the stability of the method are affected by the presence of embedded grids. The grid-embedding technique yields significant savings in computing time to achieve the same accuracy obtained wing conventional grids. (C) 1997 by Elsevier Science Inc
Decidability of predicate logics with team semantics
We study the complexity of predicate logics based on team semantics. We show
that the satisfiability problems of two-variable independence logic and
inclusion logic are both NEXPTIME-complete. Furthermore, we show that the
validity problem of two-variable dependence logic is undecidable, thereby
solving an open problem from the team semantics literature. We also briefly
analyse the complexity of the Bernays-Sch\"onfinkel-Ramsey prefix classes of
dependence logic.Comment: Extended version of a MFCS 2016 article. Changes on the earlier arXiv
version: title changed, added the result on validity of two-variable
dependence logic, restructurin
Externalizing the lateral-boundary conditions from the dynamic core in semi-implicit semi-Lagrangian models
Research is still undertaken to develop so-called transparent lateral boundary conditions (LBC) for limited-area numerical weather prediction models. In the widely used semi-implicit semi-Lagrangian schemes, this naturally leads to LBC formulations that are intrinsically intertwined with the numerics of the dynamic core. This may have profound consequences for the implementation and the maintenance of future model codes. For instance, scientific development on the dynamics may be hindered by constraints coming from today's choices in the LBC formulation and vice versa.
Building further on the work of Aidan McDonald, this paper proposes an approach where (1) the LBCs can be imposed by an extrinsic numerical scheme that is fundamentally different from the one used for the dynamic core in the interior domain and (2) substituting one such LBC scheme for another is possible in a manner that leaves the Helmholtz solver unmodified. It is argued that this concept may provide the necessary frame for formulating transparent boundary conditions in spectral limited-area models.
Since this idea touches all aspects of the LBC problem, its feasibility can only be established by a rigorous systematic approach. As a first step, this paper provides promising experimental support in a one-dimensional shallow-water model
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