Search results for "decomposition method"
showing 10 items of 29 documents
A Generalised RBF Finite Difference Approach to Solve Nonlinear Heat Conduction Problems on Unstructured Datasets
2011
Radial Basis Functions have traditionally been used to provide a continuous interpolation of scattered data sets. However, this interpolation also allows for the reconstruction of partial derivatives throughout the solution field, which can then be used to drive the solution of a partial differential equation. Since the interpolation takes place on a scattered dataset with no local connectivity, the solution is essentially meshless. RBF-based methods have been successfully used to solve a wide variety of PDEs in this fashion. Such full-domain RBF methods are highly flexible and can exhibit spectral convergence rates Madych & Nelson (1990). However, in their traditional implementation the fu…
A multi-domain approach for smoothed particle hydrodynamics simulations of highly complex flows
2018
Abstract An efficient and accurate method is proposed to solve the incompressible flow momentum and continuity equations in computational domains partitioned into subdomains in the framework of the smoothed particle hydrodynamics method. The procedure does not require any overlap of the subdomains, which would result in the increase of the computational effort. Perfectly matching solutions are obtained at the surfaces separating neighboring blocks. The block interfaces can be both planar and curved surfaces allowing to easily decompose even geometrically complex domains. The smoothing length of the kernel function is maintained constant in each subdomain, while changing between blocks where…
Three-dimensional numerical simulations on wind- and tide-induced currents: The case of Augusta Harbour (Italy)
2014
The hydrodynamic circulation in the coastal area of the Augusta Bay (Italy), located in the eastern part of Sicily, is analysed. Due to the heavy contamination generated by the several chemical and petrochemical industries active in the zone, the harbour was declared a Contaminated Site of National Interest. To mitigate the risks connected with the industrial activities located near the harbour, it is important to analyse the hydrodynamic circulation in the coastal area. To perform such analysis, a parallel 3D numerical model is used to solve the Reynolds-averaged momentum and mass balance, employing the k-e turbulence model for the Reynolds stresses. The numerical model is parallelized usi…
Two-level Schwarz method for unilateral variational inequalities
1999
The numerical solution of variational inequalities of obstacle type associated with second-order elliptic operators is considered. Iterative methods based on the domain decomposition approach are proposed for discrete obstacle problems arising from the continuous, piecewise linear finite element approximation of the differential problem. A new variant of the Schwarz methodology, called the two-level Schwarz method, is developed offering the possibility of making use of fast linear solvers (e.g., linear multigrid and fictitious domain methods) for the genuinely nonlinear obstacle problems. Namely, by using particular monotonicity results, the computational domain can be partitioned into (mes…
A New Distributed Optimization Approach for Solving CFD Design Problems Using Nash Game Coalition and Evolutionary Algorithms
2013
For decades, domain decomposition methods (DDM) have provided a way of solving large-scale problems by distributing the calculation over a number of processing units. In the case of shape optimization, this has been done for each new design introduced by the optimization algorithm. This sequential process introduces a bottleneck.
Mixed integer optimal compensation: Decompositions and mean-field approximations
2012
Mixed integer optimal compensation deals with optimizing integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this issue, we propose a decomposition method which turns the original n-dimensional problem into n independent scalar problems of lot sizing form. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon. This last reformulation step mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent s…
Acute Type Refinements of Tetrahedral Partitions of Polyhedral Domains
2001
We present a new technique to perform refinements on acute type tetrahedral partitions of a polyhedral domain, provided that the center of the circumscribed sphere around each tetrahedron belongs to the tetrahedron. The resulting family of partitions is of acute type; thus, all the tetrahedra satisfy the maximum angle condition. Both these properties are highly desirable in finite element analysis.
Multiresolution based on weighted averages of the hat function I: Linear reconstruction techniques
1998
In this paper we analyze a particular example of the general framework developed in [A. Harten, {\it SIAM J. Numer. Anal}., 33 (1996) pp. 1205--1256], the case in which the discretization operator is obtained by taking local averages with respect to the hat function. We consider a class of reconstruction procedures which are appropriate for this multiresolution setting and describe the associated prediction operators that allow us to climb up the ladder from coarse to finer levels of resolution. In Part I we use data-independent (linear) reconstruction techniques as our approximation tool. We show how to obtain multiresolution transforms in bounded domains and analyze their stability with r…
Fictitious Domain Methods for the Numerical Solution of Two-Dimensional Scattering Problems
1998
Fictitious domain methods for the numerical solution of two-dimensional scattering problems are considered. The original exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary. First-order, second-order, and exact nonreflecting boundary conditions are tested on rectangular and circular boundaries. The finite element discretizations of the corresponding approximate boundary value problems are performed using locally fitted meshes, and the discrete equations are solved with fictitious domain methods. A special finite element method using nonmatching meshes is considered. This method uses …
Parallel Schwarz methods for convection-dominated semilinear diffusion problems
2002
AbstractParallel two-level Schwarz methods are proposed for the numerical solution of convection-diffusion problems, with the emphasis on convection-dominated problems. Two variants of the methodology are investigated. They differ from each other by the type of boundary conditions (Dirichlet- or Neumann-type) posed on a part of the second-level subdomain interfaces. Convergence properties of the two-level Schwarz methods are experimentally compared with those of a variant of the standard multi-domain Schwarz alternating method. Numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods.