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Showing papers presented at "Computational Science and Engineering in 2021"


Proceedings Article
01 Mar 2021
TL;DR: In this article, a partition of unity method is used to align the local approximations with the data, and patches are adaptively refined based on local curvature. But the reconstruction of the diaphragm is not considered.
Abstract: Manual three-dimensional segmentation of medical images results in noisy data sets representing three-dimensional objects. Based on this data, we look at how to perform a smooth object reconstruction. In particular, we are interested in the diaphragm, which is a thin curved volume. We use a partition of unity method where local object representations in each patch are blended into a global reconstruction. We use principal component analysis of the local data to align the local approximations with the data. Patches are adaptively refined based on local curvature. Due to the independence of the local approximations, we can increase the resolution in the thin dimension locally in each patch. We use infinitely smooth radial basis functions (RBF) to form a level set function with the object surface as its zero level set. Least squares approximation of the location, gradients, and values outside the object is employed to handle the noise in the data set. We evaluate the resulting reconstruction in terms of residual with respect to the initial data, local curvature, and visual appearance. We present guidelines for how to choose the method parameters, and investigate how they affect the result.

1 citations


Book ChapterDOI
01 Jan 2021
TL;DR: In this paper, a general conservation law that defines a class of physical field theories is constructed, and the general field and the conservation law together correspond to a large class of relativistic hyperbolic physical field models.
Abstract: A general conservation law that defines a class of physical field theories is constructed. First, the notion of a general field is introduced as a formal sum of differential forms on a Minkowski manifold. By the action principle the conservation law is defined for such a general field. By construction, particular field notions of physics, e.g., magnetic flux, electric field strength, stress, strain etc. become instances of the general field. Hence, the differential equations that constitute physical field theories become also instances of the general conservation law. The general field and the general conservation law together correspond to a large class of relativistic hyperbolic physical field models. The parabolic and elliptic models can thereafter be derived by adding constraints. The approach creates solid foundations for developing software systems for scientific computing; the unifying structure shared by the class of field models makes it possible to implement software systems which are not restricted to certain predefined problems. The versatility of the proposed approach is demonstrated by numerical experiments with moving and deforming domains.

Book ChapterDOI
01 Jan 2021
TL;DR: In this paper, the number of similarity classes generated when the 8T-LE partition is applied to these tetrahedra was studied and it was shown that the similarity classes can be obtained by adding a new node to the body at the centroid point and then adding new nodes progressively to the centroids of faces and edges.
Abstract: The barycentric partition of a 3D-cube into tetrahedra is carried out by adding a new node to the body at the centroid point and then, new nodes are progressively added to the centroids of faces and edges. This procedure generates three types of tetrahedra in every single step called, Sommerville tetrahedron number 3 (ST3), isosceles trirectangular tetrahedron and regular right-type tetrahedron. We are interested in studying the number of similarity classes generated when the 8T-LE partition is applied to these tetrahedra.