Discrete Mesh Optimization on GPU

Zint, Daniel; Grosso, R.

doi:10.1007/978-3-030-13992-6_24

Cited by 8 publications

(2 citation statements)

References 31 publications

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“…Moreover, we compare with the hierarchical sampling strategies (HSS) [ZG18], which iteratively samples the objective function on a regular grid, identifies the best candidate sample, and refines the grid in its vicinity. The comparison is performed on 100 models since running on the whole data set is too time‐consuming (Fig.…”

Section: Methodsmentioning

confidence: 99%

Constrained Remeshing Using Evolutionary Vertex Optimization

Zhang

Wang

Guo

et al. 2022

Computer Graphics Forum

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We propose a simple yet effective method to perform surface remeshing with hard constraints, such as bounding approximation errors and ensuring Delaunay conditions. The remeshing is formulated as a constrained optimization problem, where the variables contain the mesh connectivity and the mesh geometry. To solve it effectively, we adopt traditional local operations, including edge split, edge collapse, edge flip, and vertex relocation, to update the variables. Central to our method is an evolutionary vertex optimization algorithm, which is derivative‐free and robust. The feasibility and practicability of our method are demonstrated in two applications, including error‐bounded Delaunay mesh simplification and error‐bounded angle improvement with a given number of vertices, over many models. Compared to state‐of‐the‐art methods, our method achieves higher remeshing quality.

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Section: Methodsmentioning

confidence: 99%

Constrained Remeshing Using Evolutionary Vertex Optimization

Zhang

Wang

Guo

et al. 2022

Computer Graphics Forum

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“…A survey of the literature shows that despite the introduction of recent mesh optimization strategies on GPU-based architectures, the notion of partial assembly is not present in the field of mesh optimization. This is likely because most existing methods are either developed for low-order meshes [25,26] or use a localized approach (such as Laplacian smoothing or optimization-based smoothing with a sequential patch-by-patch approach) [27,26,28,29]. In contrast to other approaches, the variational-based TMOP methods are well-suited to GPU acceleration, as all of the operations can be recast in the form of finite element computations, allowing us to take advantage of the significant GPU advances in this area.…”

Section: Introductionmentioning

confidence: 99%

Accelerating High-Order Mesh Optimization Using Finite Element Partial Assembly on GPUs

Camier¹,

Dobrev²,

Knupp³

et al. 2022

Preprint

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In this paper we present a new GPU-oriented mesh optimization method based on highorder finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high-order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU-based HPC hardware. We describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

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