87 research outputs found
Improving performance of simplified computational fluid dynamics models via symmetric successive overrelaxation
The ability to model fluid flow and heat transfer in process equipment (e.g., shell-and-tube heat exchangers) is often critical. What is more, many different geometric variants may need to be evaluated during the design process. Although this can be done using detailed computational fluid dynamics (CFD) models, the time needed to evaluate a single variant can easily reach tens of hours on powerful computing hardware. Simplified CFD models providing solutions in much shorter time frames may, therefore, be employed instead. Still, even these models can prove to be too slow or not robust enough when used in optimization algorithms. Effort is thus devoted to further improving their performance by applying the symmetric successive overrelaxation (SSOR) preconditioning technique in which, in contrast to, e.g., incomplete lower–upper factorization (ILU), the respective preconditioning matrix can always be constructed. Because the efficacy of SSOR is influenced by the selection of forward and backward relaxation factors, whose direct calculation is prohibitively expensive, their combinations are experimentally investigated using several representative meshes. Performance is then compared in terms of the single-core computational time needed to reach a converged steady-state solution, and recommendations are made regarding relaxation factor combinations generally suitable for the discussed purpose. It is shown that SSOR can be used as a suitable fallback preconditioner for the fast-performing, but numerically sensitive, incomplete lower–upper factorization
The Buffered Block Forward Backward technique for solving electromagnetic wave scattering problems
This work focuses on efficient numerical techniques for solving electromagnetic wave
scattering problems. The research is focused on three main areas: scattering from perfect
electric conductors, 2D dielectric scatterers and 3D dielectric scattering objects. The
problem of fields scattered from perfect electric conductors is formulated using the Electric
Field Integral Equation. The Coupled Field Integral Equation is used when a 2D homogeneous
dielectric object is considered. The Combined Field Integral Equation describes the
problem of scattering from 3D homogeneous dielectric objects. Discretising the Integral
Equation Formulation using the Method of Moments creates the matrix equation that is
to be solved. Due to the large number of discretisations necessary the resulting matrices
are of significant size and therefore the matrix equations cannot be solved by direct inversion
and iterative methods are employed instead. Various iterative techniques for solving
the matrix equation are presented including stationary methods such as the ”forwardbackward”
technique, as well its matrix-block version. A novel iterative solver referred to
as Buffered Block Forward Backward (BBFB) method is then described and investigated.
It is shown that the incorporation of buffer regions dampens spurious diffraction effects
and increases the computational efficiency of the algorithm. The BBFB is applied to both
perfect electric conductors and homogeneous dielectric objects. The convergence of the
BBFB method is compared to that of other techniques and it is shown that, depending on
the grouping and buffering used, it can be more effective than classical methods based on
Krylov subspaces for example. A possible application of the BBFB, namely the design of
2D dielectric photonic band-gap TeraHertz waveguides is investigated.
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Modified Preconditioned GAOR Methods for Systems of Linear Equations
Three kinds of preconditioners are proposed to accelerate the generalized AOR (GAOR) method for the linear system from the generalized least squares problem. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned generalized AOR (PGAOR) methods is better than that of the original GAOR methods. Finally, some numerical results are reported to confirm the validity of the proposed methods
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