Improved Parallel Preconditioners for Multiphysics Topology Optimizations

Akay, Hasan Umur
Oktay, Erdal
Manguoğlu, Murat
Sivas, Abdullah Ali
Topology optimization, also known as layout optimization, involves multiple physics encompassing structural, thermal, fluidic electrical and electromechanical systems including coupled phenomena such as solids and fluids as in convective cooling systems, aerodynamical systems, electronics, actuators and motors. In the root of topology optimization is the repeated solution of the finite element equations Au = f representing the physics of the problem at hand such as elasticity, heat transfer, fluid flow and electromagnetics, where A is the coefficient matrix, which is highly sparse, u is the vector of physical unknowns (displacements, temperature or velocity, etc.), f is the known source (load) vector. Numerical difficulties associated with these equations are two folds. Firstly, they are very large systems, due to large number of cells (finite elements) needed for defining a topology, requiring the use of the iterative solvers such as the conjugate gradient algorithm instead of the direct solvers. Even with that, the solution times tend to become very high, which is often tried to be resolved by parallel solution strategies. Secondly, they are extremely ill-conditioned due to highly heterogeneous material distributions that evolve during the course of topology formations, with material properties of elements varying from nearly zero values in empty regions to very large values in full regions, which is usually addressed by matrix preconditioning. When simple preconditioners, such as diagonal and incomplete LU factorization preconditioners, are used parallel efficiency deteriorate very fast due to increased number of iterations needed for convergence as more processors are used. In this paper, we modify our previous parallel topology solver implementation by introducing new matrix reordering and scaling schemes to improve the scalability of iterative solvers. We use here more sophisticated preconditioners in order to improve the parallel scalability of the iterative algorithm, even for ill-conditioned cases; not only due to heterogeneous material properties, but also due to condition number deterioration in the equations of coupled multiphysics media. The developed solver was tested for accuracy and parallel efficiency of extreme cases, demonstrating high parallel scalability.


Numerical method for conform reflection
Kushnarov, Andriy; Öktem, Hakan; Department of Scientific Computing (2010)
Conformal map has application in a lot of areas of science, e.g., fluid flow, heat conduction, solidification, electromagnetic, etc. Especially conformal map applied to elasticity theory can provide most simple and useful solution. But finding of conformal map for custom domain is not trivial problem. We used a numerical method for building a conformal map to solve torsion problem. In addition it was considered an infinite system method to solve the same problem. Results are compared.
IDER, YZ; Gençer, Nevzat Güneri; ATALAR, E; TOSUN, H (1990-03-01)
An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a crosssectional plane; therefore the axial variation of the boundary conditions and also the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward probl...
Computer simulation of grain boundary grooving and cathode voiding n bamboo interconnects by surface diffusion under capillary and electromigration forces
Akyıldız, Öncü; Oğurtanı, Tarık Ö.; Department of Metallurgical and Materials Engineering (2004)
The processes of grain boundary grooving and cathode voiding which are important in determining the life times of thin films connecting the transistors in an integrated circuit are investigated by introducing a new mathematical model, which flows from the fundamental postulates of irreversible thermodynamics, accounting for the effects of applied electric field and thermal stresses. The extensive computer studies on the triple junction displacement dynamics shows that it obeys the first order reaction kinet...
Combined centralized and decentralized fault diagnosis for discrete event systems
Karav, Ruhi; Schmidt, Şenan Ece; Schmidt, Klaus Werner; Department of Electrical and Electronics Engineering (2014)
Discrete Event Systems (DES) are used for modeling systems such as manufacturing systems, telecommunication systems and transportation systems. It is possible to incorporate the fault model in the DES model together with a fault diagnosis approach to evaluate the robustness and the reliability of the system at the design stage. There are centralized or decentralized fault diagnosis approaches in the literature. The centralized fault diagnosis achieves stronger results however it does not scale to reasonably...
Accurate multimode vibrational calculations using a B-spline basis: theory, tests and application to dioxirane and diazirinone
Toffolı, Danıele; Sparta, Manuel; Christiansen, Ove (2011-01-01)
The use of B-spline basis sets is explored in the context of a vibrational program for automatic potential energy surface (PES) construction and multimode anharmonic vibrational wave function calculation. Results are compared with calculations using localized Gaussians and harmonic oscillator basis functions. Potential energy surfaces are constructed in an iterative fashion using a recently developed adaptive density-guided approach. The basis set requirements for an accurate representation of the vibration...
Citation Formats
H. U. Akay, E. Oktay, M. Manguoğlu, and A. A. Sivas, “Improved Parallel Preconditioners for Multiphysics Topology Optimizations,” presented at the 27th International Conference on Parallel Computational Fluid Dynamics (17 - 20 Mayıs 2015), Montreal, Canada, 2015, Accessed: 00, 2021. [Online]. Available: