This review paper provides an overview of different level-set methods for structural topology
optimization. Level-set methods can be categorized with respect to the level-set-function …

In this paper, we introduce a new approach based on distance fields to exactly impose
boundary conditions in physics-informed deep neural networks. The challenges in satisfying …

In the past two decades, meshfree methods have emerged into a new class of computational
methods with considerable success. In addition, a significant amount of progress has been …

This paper presents a compact and efficient 88-line MATLAB code for the parameterized
level set method based topology optimization using radial basis functions (RBFs), which is …

We propose the use of nonlocal operators to define new types of flows and functionals for
image processing and elsewhere. A main advantage over classical PDE-based algorithms …

In an attempt to introduce application scientists and graduate students to the exciting topic of
positive definite kernels and radial basis functions, this book presents modern theoretical …

Level set methods have become an attractive design tool in shape and topology
optimization for obtaining lighter and more efficient structures. In this paper, the popular …

In standard equispaced finite difference (FD) formulas, symmetries can make the order of
accuracy relatively high compared to the number of nodes in the FD stencil. With scattered …

Kernels are valuable tools in various fields of numerical analysis, including approximation,
interpolation, meshless methods for solving partial differential equations, neural networks …

This paper presents an effective parametric approach by extending the conventional level
set method to structural shape and topology optimization using the compactly supported …