Computer Methods in Applied Mechanics and Engineering
Communications of the ACM
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Multigrid
The C++ Programming Language, Third Edition
The C++ Programming Language, Third Edition
SIAM Journal on Optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Preconditioner for Substructuring Based on Constrained Energy Minimization
SIAM Journal on Scientific Computing
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Validity of the single processor approach to achieving large scale computing capabilities
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
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The complexity of problems attacked in topology optimization has increased dramatically during the past decade. Examples include fully coupled multiphysics problems in thermo-elasticity, fluid-structure interaction, Micro-Electro Mechanical System (MEMS) design and large-scale three dimensional problems. The only feasible way to obtain a solution within a reasonable amount of time is to use parallel computations in order to speed up the solution process. The focus of this article is on a fully parallel topology optimization framework implemented in C++, with emphasis on utilizing well tested and simple to implement linear solvers and optimization algorithms. However, to ensure generality, the code is developed to be easily extendable in terms of physical models as well as in terms of solution methods, without compromising the parallel scalability. The widely used Method of Moving Asymptotes optimization algorithm is parallelized and included as a fundamental part of the code. The capabilities of the presented approaches are demonstrated on topology optimization of a Stokes flow problem with target outflow constraints as well as the minimum compliance problem with a volume constraint from linear elasticity.