Tree Structures for Adaptive Control Space in 3D Meshing

The article presents a comparison of several octree- and kd-tree-based structuresused for the construction of control space in the process of anisotropicmesh generation and adaptation. The adaptive control space utilized by theauthors supervises the construction of meshes by providing the required metricinformation regarding the desired shape and size of elements of the mesh ateach point of the modeled domain. Comparative tests of these auxiliary structureswere carried out based on different versions of the tree structures withrespect to computational and memory complexity as well as the quality of thegenerated mesh. Analysis of the results shows that kd-trees (not present inthe meshing literature in this role) offer good performance and may becomea reasonable alternative to octree structures

Symbolic Block Decomposition In Hexahedral Mesh Generation

Hexahedral mesh generation for three-dimensional solid objects is often done in stages. Usually an object is first subdivided into simple-shaped subregions, which then are filled withhexahedral finite elements. This article presents an automatic subdividing method of polyhedron with planar faces. The subdivision is based on medial surface, axes and nodes of a solid.The main emphasis is put on creating a topology of subregions. Obtaining such a topologyinvolves defining a graph structure OMG which contains necessary information about medialsurface topology and object topology, followed by simple symbolic processing on it

VISIBILITY DETERMINATION IN BEAM TRACING WITH APPLICATION TO REAL-TIME SOUND SIMULATION

The work presents some aspects of beam tracing technique used in sound simulation. Adaptive Frustum algorithm, which was designed for detecting obstacles via beam subdivision was reviewed from efficiency point of view as well asfor its accuracy. Some possible improvements are suggested, however, they donot fully solve the problems of using this algorithm in real-time applications.Improved algorithm implementation was tested on five scenes with differentcharacteristics and varying complexity

DEFINITION AND INTERPOLATION OF DISCRETE METRIC FOR MESH GENERATION ON 3D SURFACES

The article concerns the problem of a definition of the control space from a set of discretedata (metric description gathered from different sources) and its influence on the efficiency ofthe generation process with respect to 2D and 3D surface meshes. Several methods of metricinterpolation between these discrete points are inspected, including an automated selectionof proper method. Some aspects of the procedures of creation and employment of the meshcontrol space based on the discrete set of points are presented. The results of using differentvariations of these methods are also included

Tree-based Control Space Structures for Discrete Metric Sources in 3D Meshing

This article compares the different variations of the octree and kd-tree structures used to create a control space based on a set of discrete metric point-sources. The control space thus created supervises the generation of the mesh providing efficient access to the required information on the desired shape and size of the mesh elements at each point of the discretized domain. Structures are compared in terms of computational and memory complexity as well as regarding the accuracy of the approximation of the set of discrete metric sources in the created control space structure

Definition and interpolation of discrete metric for mesh generation on 3D surfaces Definicja i interpolacja dyskretnej metryki dla tworzenia siatek na powierzchniach trójwymiarowych /

Tyt. z nagłówka.Bibliografia s. 102-103.Dostępny również w formie drukowanej.STRESZCZENIE: Artykuł opisuje zagadnienie definicji przestrzeni kontrolnej (sterującej procesem generowania siatek) na podstawie dyskretnych danych (opisu metryki pozyskanego z różnych zródeł) oraz jej wpływu na wydajność procesu generacji siatek na płaszczyźnie oraz powierzchniach trójwymiarowych. Rozpatrywane są różne metody interpolacji metryki w obszarach pomiędzy dyskretnymi punktami ze zdefiniowaną metryką, włącznie z automatyczną metodą wyboru odpowiedniej metody interpolacji. Przedstawione są zagadnienia związane z procesem tworzenia i wykorzystywania przestrzeni kontrolnej opartej na informacji z dyskretnego zbioru punktów. Załączone są także przykładowe wyniki zastosowania różnych wariantów opisywanych metod. SŁOWA KLUCZOWE: generacja siatek, powierzchnie parametryczne, dyskretna metryka, triangulacja Delaunaya, ABSTRACT: The article concerns the problem of a definition of the control space from a set of discrete data (metric description gathered from different sources) and its influence on the efficiency of the generation process with respect to 2D and 3D surface meshes. Several methods of metric interpolation between these discrete points are inspected, including an automated selection of proper method. Some aspects of the procedures of creation and employment of the mesh control space based on the discrete set of points are presented. The results of using different variations of these methods are also included. KEYWORDS: mesh generation, parametric surface, discrete metric, Delaunay triangulation

Overview of Adaptive and Low-Rank Approximation Algorithms for Modeling of The Influence of Electromagnetic Waves Generated by The Cell Phone Antenna on The Human Head

This paper presents an overview of formulations and algorithms dedicated to modeling the influence of electromagnetic waves on the human head. We start from the three-dimensional MRI scan of the human head. We approximate the MRI scan by the continuous approximation span over three-dimensional h adaptive mesh with quadratic polynomials. Next, we introduce time-harmonic Maxwell equations with a 1.8 GHz cell-phone antenna. We solve the problem of the propagation of electromagnetic waves on the human head. We compute the specific absorption rate used as the heat source for the Pennes bioheat equation. Finally, we introduce the Pennes bio-heat equation modeling the heat generated by the electromagnetic waves propagating through the skull, tissue, and air layers in the human head. We discuss the discretization and time-stepping algorithm for the Pennes equation’s solution over the human head. Namely, we focus on the Crank-Nicolson time integration scheme, to solve the bioheat transfer equations. We employ the hp finite elements with hierarchical shape functions and hp adaptive algorithm in three-dimensions. We propose an adaptive algorithm mixed with time-stepping iterations, where we simultaneously adapt the computational mesh, solve the Maxwell and Pennes equations, and we iterative with time steps. We employ the sparse Gaussian elimination algorithm with low-rank compression of the off-diagonal matrix blocks for the factorization of matrices. We conclude with the statement that 15 minutes of talk with a 1.8 GHz antenna of 1 Wat power results in increased brain tissue temperature up to 38.4 Celsius degree

DEFINITION AND INTERPOLATION OF DISCRETE

The article concerns the problem of a definition of the control space from a set of discrete data (metric description gathered from different sources) and its influence on the efficiency of the generation process with respect to 2D and 3D surface meshes. Several methods of metric interpolation between these discrete points are inspected, including an automated selection of proper method. Some aspects of the procedures of creation and employment of the mesh control space based on the discrete set of points are presented. The results of using different variations of these methods are also included