Efficient distributed approach for density-based topology optimization using coarsening and h-refinement

This work presents an efficient parallel implementation of density-based topology optimization using Adaptive Mesh Refinement (AMR) schemes to reduce the computational burden of the bottleneck of the process, the evaluation of the objective function using Finite Element Analysis (FEA). The objective is to obtain an equivalent design to the one generated on a uniformly fine mesh using distributed memory computing but at a much cheaper computational cost. We propose using a fine mesh for the optimization and a coarse mesh for the analysis using coarsening and refinement criteria based on the thresholding of design variables. We evaluate the functional on the coarse mesh using a distributed conjugate gradient solver preconditioned by an algebraic multigrid (AMG) method showing its computational advantages in some cases by comparing with geometric multigrid (GMG) and AMG methods in two- and three-dimensional problems. We use different computational resources with small regularization distances for such comparisons. We also evaluate the performance and scalability of the proposal using a different number of computing cores and distributed computing hosts. The numerical results show a significant increment of the computing performance for the overall computing time of the proposal combining dynamic coarsening, adaptive mesh refinement, and distributed memory computing architecturesThis work has been supported by the AEI/FEDER and UE under the contract DPI2016-77538-R

An Adjoint‐Based Solver with Adaptive Mesh Refinement For Efficient Design of Coupled Thermal‐Fluid Systems

A multi-objective continuous adjoint strategy based on the superposition of boundary functions for topology optimization of problems where the heat transfer must be enhanced and the dissipated mechanical power controlled at the same time, has been here implemented in a Finite Volume (FV), incompressible, steady flow solver supporting a dynamic Adaptive Mesh Refinement (AMR) strategy. The solver models the transition from fluid to solid by a porosity field, that appears in the form of penalization in the momentum equation; the material distribution is optimized by the Method of Moving Asymptotes (MMA). AMR is based on a hierarchical non-conforming h-refinement strategy and is applied together with a flux correction to enforce conservation across topology changes. It is shown that a proper choice of the refinement criterium favors a mesh-independent solution. Finally, a Pareto front built from the components of the objective function is used to find the best combination of the weights in the optimization cycle. Numerical experiments on two- and three-dimensional test cases, including the aero-thermal optimization of a simplified layout of a cooling system, have been used to validate the implemented methodology

A Variational r-Adaption and Shape-Optimization Method for Finite-Deformation Elasticity

This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configuration forces for isoparametric elements and nonlinear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and nonlinear elastic bodies; and the optimization of the shape of elastic inclusions

Semantically Informed Multiview Surface Refinement

We present a method to jointly refine the geometry and semantic segmentation of 3D surface meshes. Our method alternates between updating the shape and the semantic labels. In the geometry refinement step, the mesh is deformed with variational energy minimization, such that it simultaneously maximizes photo-consistency and the compatibility of the semantic segmentations across a set of calibrated images. Label-specific shape priors account for interactions between the geometry and the semantic labels in 3D. In the semantic segmentation step, the labels on the mesh are updated with MRF inference, such that they are compatible with the semantic segmentations in the input images. Also, this step includes prior assumptions about the surface shape of different semantic classes. The priors induce a tight coupling, where semantic information influences the shape update and vice versa. Specifically, we introduce priors that favor (i) adaptive smoothing, depending on the class label; (ii) straightness of class boundaries; and (iii) semantic labels that are consistent with the surface orientation. The novel mesh-based reconstruction is evaluated in a series of experiments with real and synthetic data. We compare both to state-of-the-art, voxel-based semantic 3D reconstruction, and to purely geometric mesh refinement, and demonstrate that the proposed scheme yields improved 3D geometry as well as an improved semantic segmentation

Scalable wavelet-based coding of irregular meshes with interactive region-of-interest support

This paper proposes a novel functionality in wavelet-based irregular mesh coding, which is interactive region-of-interest (ROI) support. The proposed approach enables the user to define the arbitrary ROIs at the decoder side and to prioritize and decode these regions at arbitrarily high-granularity levels. In this context, a novel adaptive wavelet transform for irregular meshes is proposed, which enables: 1) varying the resolution across the surface at arbitrarily fine-granularity levels and 2) dynamic tiling, which adapts the tile sizes to the local sampling densities at each resolution level. The proposed tiling approach enables a rate-distortion-optimal distribution of rate across spatial regions. When limiting the highest resolution ROI to the visible regions, the fine granularity of the proposed adaptive wavelet transform reduces the required amount of graphics memory by up to 50%. Furthermore, the required graphics memory for an arbitrary small ROI becomes negligible compared to rendering without ROI support, independent of any tiling decisions. Random access is provided by a novel dynamic tiling approach, which proves to be particularly beneficial for large models of over 10(6) similar to 10(7) vertices. The experiments show that the dynamic tiling introduces a limited lossless rate penalty compared to an equivalent codec without ROI support. Additionally, rate savings up to 85% are observed while decoding ROIs of tens of thousands of vertices

Recursive Algorithms for Distributed Forests of Octrees

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not often exploited in previously published mesh-related algorithms. This is because the branches are not explicitly stored, and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work we combine hierarchical and topological relationships between octree branches to design efficient recursive algorithms. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a domain partition, as well as every interface (face, edge and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order $C^0$ nodal basis functions. We analyze the complexity of the new recursive algorithms theoretically, and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458k cores of the JUQUEEN supercomputer.Comment: 35 pages, 15 figures, 3 table