Search results for "Domain decomposition methods"
showing 10 items of 18 documents
Domain decomposition in the symmetric boundary element analysis
2002
Recent developments in the symmetric boundary element method (SBEM) have shown a clear superiority of this formulation over the collocation method. Its competitiveness has been tested in comparison to the finite element method (FEM) and is manifested in several engineering problems in which internal boundaries are present, i.e. those in which the body shows a jump in the physical characteristics of the material and in which an appropriate study of the response must be used. When we work in the ambit of the SBE formulation, the body is subdivided into macroelements characterized by some relations which link the interface boundary unknowns to the external actions. These relations, valid for e…
Multidomain boundary integral formulation for piezoelectric materials fracture mechanics
2001
Abstract A boundary element method and its numerical implementation for the analysis of piezoelectric materials are presented with the aim to exploit their features in linear electroelastic fracture mechanics. The problem is formulated employing generalized displacements, that is displacements and electric potential, and generalized tractions, that is tractions and electric displacement. The generalized displacements boundary integral equation is obtained by using the closed form of the piezoelasticity fundamental solutions. These are derived through a displacement based modified Lekhnitskii’s functions approach. The multidomain boundary element technique is implemented to achieve the numer…
Numerical Algorithms Based on Characteristic Domain Decomposition for Obstacle Problems
1997
A new numerical solution algorithm for obstacle problems is proposed, where the characteristic domain decomposition into active and inactive subdomains separated by the free boundary is approximated by a Schwarz method. Such an approach gives an opportunity to apply fast linear system solvers to genuinely non-linear obstacle problems. Other solution algorithms, like projected relaxation methods and active set strategies, are compared to the new solution algorithm. Numerical experiments related to the elastoplastic torsion problem are included showing the efficiency of the new approach.
Boundary elements analysis of adhesively bonded piezoelectric active repair
2009
Abstract This paper presents the analysis of active piezoelectric patches for cracked structures by the boundary element method. A two-dimensional boundary integral formulation based on the multidomain technique is used to model cracks and to assemble the multi-layered piezoelectric patches to the host damaged structures. The fracture mechanics behavior of the repaired structures is analyzed for both perfect and imperfect interface between patches and host beams. The imperfect interface, representing the adhesive between two different layers, is modeled by using a “spring model” that involves linear relationships between the interface tractions, in normal and tangential directions, and the …
Exploiting seeding of random number generators for efficient domain decomposition parallelization of dissipative particle dynamics
2013
Abstract Dissipative particle dynamics (DPD) is a new promising method commonly used in coarse-grained simulations of soft matter and biomolecular systems at constant temperature. The DPD thermostat involves the evaluation of stochastic or random forces between pairs of neighboring particles in every time step. In a parallel computing environment, the transfer of these forces from node to node can be very time consuming. In this paper we describe the implementation of a seeded random number generator with three input seeds at each step which enables the complete generation of the pairwise stochastic forces in parallel DPD simulations with minimal communication between nodes.
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.