Related papers: Using trullekrul in pde2path -- anisotropic mesh a…
In this note we present concrete applications of the general treatment of anisotropic thermo-elasticity developed in Part I.
pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on…
This article presents an introduction to MMPDElab, a package written in MATLAB for adaptive mesh movement and adaptive moving mesh P1 finite element solution of second-order partial different equations having continuous solutions in one,…
Several applications in astrophysics require adequately resolving many physical and temporal scales which vary over several orders of magnitude. Adaptive mesh refinement techniques address this problem effectively but often result in…
In this note we develop tools and techniques for the treatment of anisotropic thermo-elasticity in two space dimensions. We use a diagonalisation technique to obtain properties of the characteristic roots of the full symbol of the system in…
Anisotropic mesh quality measures and anisotropic mesh adaptation are studied for polygonal meshes. Three sets of alignment and equidistribution measures are developed, one based on least squares fitting, one based on generalized…
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…
Understanding the phase transition mechanisms in two-dimensional (2D) materials is a key to precisely tailor their properties at the nanoscale. Molybdenum ditelluride (MoTe2) exhibits multiple phases at room temperature, making it a…
Despite decades of research in this area, mesh adaptation capabilities are still rarely found in numerical simulation software. We postulate that the primary reason for this is lack of usability. Integrating mesh adaptation into existing…
This paper aims to demonstrate the applicability of the L_2-integral transform to Partial Differential Equations (PDEs). Of special interest is section (6), which contains an application of the L_2-transform to a PDE of exponential squared…
We introduce the Macaulay2 package $\mathtt{LinearTruncations}$ for finding and studying the truncations of a multigraded module over a standard multigraded ring that have linear resolutions.
With the advancement of computer vision, dynamic 3D reconstruction techniques have seen significant progress and found applications in various fields. However, these techniques generate large amounts of 3D data sequences, necessitating…
We developed the pycraf Python package, which provides functions and procedures for various tasks related to spectrum-management compatibility studies. This includes an implementation of ITU-R Rec. P.452, which allows to calculate the path…
We explain some pde2path setups for pattern formation in 1D, 2D and 3D. A focus is on new pde2path functions for branch switching at steady bifurcation points of higher multiplicity, typically due to discrete symmetries, but we also review…
The As-Rigid-As-Possible (ARAP) shape deformation framework is a versatile technique for morphing, surface modelling, and mesh editing. We discuss an improvement of the ARAP framework in a few aspects: 1. Given a triangular mesh in 3D…
We introduce a computational method and a user-friendly code with a terminal-based graphical user interface (GUI), named ElATools, developed to analyze mechanical and anisotropic elastic properties. ElATools enables facile analysis of the…
We have developed a graphical user interface (GUI) based package $\mu$2mech to perform phase-field simulation for predicting microstructure evolution. The package can take inputs from ab initio calculations and CALPHAD (Calculation of Phase…
Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…
Spectroscopic ellipsometry (SE) has emerged as a powerful and non-destructive optical characterization technique for probing the complex dielectric properties of two-dimensional (2D) materials. This review provides a comprehensive overview…
Plasmonic waveguides based on 2D materials, which enable the formations of guided modes confined around few-layered material, are promising plasmonic platforms for the miniaturization of photonic devices. Nonetheless, such waveguides…