An Unfitted dG Scheme for Coupled Bulk-Surface PDEs on Complex Geometries

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christian Engwer ◽  
Sebastian Westerheide
Keyword(s):  
Curved Surfaces ◽  
Continuity Equations ◽  
Cut Cell ◽  
Higher Dimensional ◽  
Bulk Surface ◽  
Surface Models ◽  
Discrete Analogues ◽  
Phd Thesis ◽  
High Degree ◽  
Theoretical Results

Abstract The unfitted discontinuous Galerkin (UDG) method allows for conservative dG discretizations of partial differential equations (PDEs) based on cut cell meshes. It is hence particularly suitable for solving continuity equations on complex-shaped bulk domains. In this paper based on and extending the PhD thesis of the second author, we show how the method can be transferred to PDEs on curved surfaces. Motivated by a class of biological model problems comprising continuity equations on a static bulk domain and its surface, we propose a new UDG scheme for bulk-surface models. The method combines ideas of extending surface PDEs to higher-dimensional bulk domains with concepts of trace finite element methods. A particular focus is given to the necessary steps to retain discrete analogues to conservation laws of the discretized PDEs. A high degree of geometric flexibility is achieved by using a level set representation of the geometry. We present theoretical results to prove stability of the method and to investigate its conservation properties. Convergence is shown in an energy norm and numerical results show optimal convergence order in bulk/surface H 1 {H^{1}} - and L 2 {L^{2}} -norms.

scholarly journals CONSISTENT MULTI-VIEW TEXTURING OF DETAILED 3D SURFACE MODELS

2015 ◽  
Vol II-3/W4 ◽  
pp. 25-31 ◽  
Author(s):  
K. Davydova ◽  
G. Kuschk ◽  
L. Hoegner ◽  
P. Reinartz ◽  
U. Stilla
Keyword(s):  
Large Scale ◽  
Texture Mapping ◽  
Aerial Images ◽  
Field Energy ◽  
Multiple Camera ◽  
3D Surface ◽  
Surface Models ◽  
Mapping Techniques ◽  
3D Scene ◽  
High Degree

Texture mapping techniques are used to achieve a high degree of realism for computer generated large-scale and detailed 3D surface models by extracting the texture information from photographic images and applying it to the object surfaces. Due to the fact that a single image cannot capture all parts of the scene, a number of images should be taken. However, texturing the object surfaces from several images can lead to lighting variations between the neighboring texture fragments. In this paper we describe the creation of a textured 3D scene from overlapping aerial images using a Markov Random Field energy minimization framework. We aim to maximize the quality of the generated texture mosaic, preserving the resolution from the original images, and at the same time to minimize the seam visibilities between adjacent fragments. As input data we use a triangulated mesh of the city center of Munich and multiple camera views of the scene from different directions.

Multivariate Linear Rational Expectations Models

1997 ◽  
Vol 13 (6) ◽  
pp. 877-888 ◽  
Author(s):  
Michael Binder ◽  
M. Hashem Pesaran
Keyword(s):  
Rational Expectations ◽  
Stable Solution ◽  
Future Expectations ◽  
Determinantal Equation ◽  
Fast Determination ◽  
Recursive Solution ◽  
Dependent Variables ◽  
High Degree ◽  
Theoretical Results

This paper considers the solution of multivariate linear rational expectations models. It is described how all possible classes of solutions (namely, the unique stable solution, multiple stable solutions, and the case where no stable solution exists) of such models can be characterized using the quadratic determinantal equation (QDE) method of Binder and Pesaran (1995, in M.H. Pesaran & M. Wickens [eds.], Handbook of Applied Econometrics: Macroeconomics, pp. 139–187. Oxford: Basil Blackwell). To this end, some further theoretical results regarding the QDE method expanding on previous work are presented. In addition, numerical techniques are discussed allowing reasonably fast determination of the dimension of the solution set of the model under consideration using the QDE method. The paper also proposes a new, fully recursive solution method for models involving lagged dependent variables and current and future expectations. This new method is entirely straightforward to implement, fast, and applicable also to high-dimensional problems possibly involving coefficient matrices with a high degree of singularity.

Theoretical and Experimental Vibration Analyses of Trapezoidal and Sinusoidal Corrugated Plates

2012 ◽  
Author(s):  
Adil Yucel ◽  
Alaeddin Arpaci
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Analysis Technique ◽  
Surface Models ◽  
Section Profile ◽  
Corrugated Plates ◽  
Cross Section Profile ◽  
Manufacturing Parameters ◽  
Theoretical Results

In this study, dynamic behaviour of trapezoidal and sinusoidal corrugated plates which are widely used in the fields of space, aviation, automotive, construction and shipbuilding have been analyzed. 330 different surface models varying according to corrugation height and number have been created for these plates which have various manufacturing parameters. At this stage, the number of analyses is 660. These models have been analyzed for different boundary conditions and modal analyses to obtain natural frequencies and mode shapes have been conducted using finite element method. In addition, changes in the trapezoidal cross-section profile have also been investigated by analyzing 38 different plates with varying cross-section profiles. Examining these results, the effects of corrugation height and number on natural frequencies and mode shapes have been determined. As a result of the study a total of 368 drawings were prepared and 736 analyses were performed. Besides, the theoretical results have been verified using the experimental modal analysis technique for some selected models which are being manufactured in the market.

Robust Design: Goal Formulations and a Comparison of Metamodeling Methods

1999 ◽  
Author(s):  
Yao Lin ◽  
Kiran Krishnapur ◽  
Janet K. Allen ◽  
Farrokh Mistree
Keyword(s):  
Response Surface ◽  
Robust Design ◽  
Design Space ◽  
Response Surface Models ◽  
Design Variables ◽  
Nonlinear Design ◽  
Highly Nonlinear ◽  
Variable Function ◽  
Surface Models ◽  
High Degree

Abstract In this paper, through theoretical analysis, we point out the limitations of goal formulations in previous methods for approximation-based robust design. Based on different philosophies and mathematical deduction, we propose three new methods to formulate robust design goals. Using a single variable function, we compare and contrast the use of response surface models and kriging models for approximating non-random, deterministic computer analyses in robust design with large variances of design variables in a highly nonlinear design space. Our preliminary conclusions are: 1) kriging models perform better than response surface models in a large design space with a high degree of nonlinearity, and 2) more robust solutions are achievable with kriging models than with response surface models.

scholarly journals Nonradial Pulsation among δ Scuti Stars

1993 ◽  
Vol 139 ◽  
pp. 135-143
Author(s):  
Michel Breger
Keyword(s):  
Stellar Evolution ◽  
Single Mode ◽  
Period Change ◽  
Evolutionary Changes ◽  
High Degree ◽  
Scuti Stars ◽  
Larger Sample ◽  
Δ Scuti Stars ◽  
Nonradial Pulsation ◽  
Theoretical Results

AbstractThe review examines recent observational and theoretical results on the nonradial pulsation of δ Scuti stars. The dominant pulsation modes are rotationally split p modes with = 1 and 2, and radial orders 1 to 4. Line-profile analyses also reveal the existence of additional high-degree modes. Nonradial pulsation is usually accompanied by slow amplitude and period variability. The small-amplitude single-mode variables are shown to be typical nonradial pulsators.The interesting cases of 1 Mon and θ2 Tau are examined in more detail. The present status of asteroseismolgy of the δ Scuti stars is reviewed.The periods of the four evolved δ Scuti variables studied are found to be decreasing, although stellar evolution predicts period increases due to larger radii. New work on the multiple periods of AI Vel shows that, apart from stellar evolution, an additional mechanism must exist to cause temporary period changes. It is argued that for a larger sample of stars the average period change must nevertheless reflect evolutionary changes.

scholarly journals Role of correlations in two-neutron transfer reactions

2019 ◽  
Vol 223 ◽  
pp. 01035
Author(s):  
Jesus Lubian ◽  
Jonas L. Ferreira ◽  
Roberto Linares ◽  
Erica N. Cardozo ◽  
Barbara Paes ◽  
...  
Keyword(s):  
Experimental Data ◽  
Angular Distribution ◽  
Cross Sections ◽  
Incident Energy ◽  
Transfer Reactions ◽  
Neutron Transfer ◽  
Pairing Correlation ◽  
High Degree ◽  
Theoretical Results

This work presents theoretical results compared with the experimental data for the two–neutron transfer angular distribution in which a beam of 18O nucleus, at 84 MeV incident energy, has collided onthe 13C, 28Si, and 64Ni targets. The two-neutron transfer in the 9Be(7Be,9Be)7Be reaction, at 23.1 MeV incident energy, was also analyzed. The main goal was to verify the relevance of the pairing correlation of the two transferred neutrons on the cross sections and to show its role when both neutrons are transferred to states with a low and high degree of collectivity.

scholarly journals SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS

2021 ◽  
pp. 1-52
Author(s):  
Agustin Moreno
Keyword(s):  
Field Theory ◽  
Intersection Theory ◽  
Holomorphic Curves ◽  
Perturbation Scheme ◽  
Contact Manifolds ◽  
Higher Dimensional ◽  
Symplectic Field Theory ◽  
Phd Thesis ◽  
Symplectic Cobordisms

Abstract I construct infinitely many nondiffeomorphic examples of $5$ -dimensional contact manifolds which are tight, admit no strong fillings and do not have Giroux torsion. I obtain obstruction results for symplectic cobordisms, for which I give a proof not relying on the polyfold abstract perturbation scheme for Symplectic Field Theory (SFT). These results are part of my PhD thesis [23], and are the first applications of higher-dimensional Siefring intersection theory for holomorphic curves and hypersurfaces, as outlined in [23, 24], as a prequel to [30].

The Modified LS-STAG Method Application for Planar Viscoelastic Flow Computation in a 4:1 Contraction Channel

2021 ◽  
pp. 46-63
Author(s):  
I.K. Marchevsky ◽  
V.V. Puzikova
Keyword(s):  
Software Package ◽  
Incompressible Flows ◽  
Weissenberg Number ◽  
Immersed Boundary ◽  
Time Stepping ◽  
Cut Cell ◽  
Discrete Analogues ◽  
Predictor Corrector ◽  
Benchmark Solutions ◽  
Rate Type

In this study we present the modification of the LS-STAG immersed boundary cut-cell method. This modification is designed for viscoelastic fluids. Linear and quasilinear viscoelastic fluid models of a rate type are considered. The obtained numerical method is implemented in the LS-STAG software package developed by the author. This software is created for viscous incompressible flows simulation both by the LS-STAG method and by it developed modifications. Besides of this, the software package is designed to compute extra-stresses for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson --- Segalman fluids on the LS-STAG mesh. The construction of convective derivatives discrete analogues is described for Oldroyd, Cotter --- Rivlin, Jaumann --- Zaremba --- Noll derivatives. The centers of base LS-STAG mesh cells are the locations for shear non-Newtonian stresses computation. The corners of these cells are the positions for normal non-Newtonian stresses computation. The first order predictor--corrector scheme is the basis for time-stepping numerical algorithm. Benchmark solutions for the planar flow of Oldroyd-B fluid in a 4:1 contraction channel are presented. A critical value of Weissenberg number is defined. Computational results are in good agreement with the data known in the literature

HETEROCLINICAL REPELLERS IMPLY CHAOS

2006 ◽  
Vol 16 (05) ◽  
pp. 1471-1489 ◽  
Author(s):  
WEI LIN ◽  
GUANRONG CHEN
Keyword(s):  
Discrete Systems ◽  
Higher Dimensional ◽  
Theoretical Results

In this paper, we prove that chaos in the sense of Li–Yorke and of Devaney is prevalent in discrete systems admitting the so-called heteroclinical repellers, which are similar to the transversely heteroclinical orbits in both continuous and discrete systems and are corresponding to the snap-back repeller proposed by Marotto for proving the existence of chaos in higher-dimensional systems. In addition, the concept of heteroclinical repellers is generalized to be applicable to the case with degenerate transformations. In the end, some illustrative examples are provided to illustrate the theoretical results.

scholarly journals On Special forms of Splicing on Arrays and Graphs

Triangle ◽  
2018 ◽  
pp. 119
Author(s):  
K. G. Subramanian ◽  
A. Roslin Sagaya Mary ◽  
P. Helen Chandra
Keyword(s):  
Dna Computing ◽  
Formal Language ◽  
Restriction Enzymes ◽  
Great Depth ◽  
Formal Language Theory ◽  
Language Theory ◽  
Dna Molecules ◽  
Higher Dimensional ◽  
Theoretical Results ◽  
Theory Extension

Tom Head (1987), in his pioneering work on formal language theory applied to DNA computing, introduced a new operation of splicing on strings, while proposing a model of certain recombination behaviour of DNA molecules under the action of restriction enzymes and ligases. Since then this operation has been studied in great depth giving rise to a number of theoretical results of great interest in formal language theory. Extension of this operation of splicing to higher dimensional structures such as circular words, arrays, trees and graphs have been proposed in the literature. Here we examine the effect of certain specific forms of the splicing operation applied to arrays and graphs.

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