Related papers: High-Order Mesh Morphing for Boundary and Interfac…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
We propose a method to modify a polygonal mesh in order to fit the zero-isoline of a level set function by extending a standard body-fitted strategy to a tessellation with arbitrarily-shaped elements. The novel level set-fitted approach, in…
An accurate implicit description of geometries is enabled by the level-set method. Level-set data is given at the nodes of a higher-order background mesh and the interpolated zero-level sets imply boundaries of the domain or interfaces…
The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…
High-order quadrilateral meshes offer superior accuracy and computational efficiency in numerical simulations. However, existing methods struggle to simultaneously preserve boundary/interface features, ensure high quality, and achieve…
This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high…
During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…
This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…
In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that…
Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…
As an important metric for mesh quality evaluation, the isotropy property holds significant value for applications such as texture UV-mapping, physical simulation, and discrete geometric analysis. Classical isotropy remeshing methods adjust…
This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…
As feature sizes shrink to the nanometer scale, accurately transferring circuit patterns from photomasks to silicon wafers becomes increasingly challenging. Optical proximity correction (OPC) is widely used to ensure pattern fidelity and…
In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…
Designing a freeform surface to reflect or refract light to achieve a target distribution is a challenging inverse problem. In this paper, we propose an end-to-end optimization strategy for an optical surface mesh. Our formulation leverages…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…