scholarly journals Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems with Rough Data

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Konrad Simon ◽  
Jörn Behrens
Keyword(s):  
Nonlinear Problems ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Multiscale Methods ◽  
Galerkin Methods ◽  
Standard Methods ◽  
Multiscale Problems ◽  
Eulerian Method ◽  
Lower Order Terms ◽  
New Framework

AbstractWe introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when the model involves dominant lower order terms. Our idea to overcome the associated difficulties is a semi-Lagrangian based reconstruction of subgrid variability into a multiscale basis by solving many local inverse problems. Globally the method looks like a Eulerian method with multiscale stabilized basis. We show example runs in one and two dimensions and a comparison to standard methods to support our ideas and discuss possible extensions to other types of Galerkin methods, higher dimensions and nonlinear problems.

scholarly journals TIME ACCURATE FAST THREE-STEP WAVELET-GALERKIN METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 04 (01) ◽  
pp. 65-79 ◽  
Author(s):  
MANI MEHRA ◽  
B. V. RATHISH KUMAR
Keyword(s):  
Galerkin Method ◽  
Numerical Experiments ◽  
Nonlinear Problems ◽  
Taylor Series Expansion ◽  
Two Dimensions ◽  
One Dimension ◽  
Advection Equation ◽  
Galerkin Methods ◽  
Present Scheme ◽  
Wavelet Galerkin Method

We introduce the concept of three-step wavelet-Galerkin method based on the Taylor series expansion in time. Unlike the Taylor–Galerkin methods, the present scheme does not contain any new higher-order derivatives which makes it suitable for solving nonlinear problems. Numerical schemes taking advantage of the wavelet bases capabilities to compress the operators and sparse representation of functions which are smooth, except for localized regions, up to any given accuracy are presented. Here numerical experiments deal with advection equation with the spiky solution in one dimension, two dimensions and nonlinear equation with a shock in solution in two dimensions. Numerical results indicate the versatility and effectiveness of the proposed scheme.

Classifying B2B Inter-Organizational Information Systems

2005 ◽  
pp. 55-75
Author(s):  
B. Ilyoo
Keyword(s):  
Business Strategy ◽  
Two Dimensions ◽  
Organizational Systems ◽  
System Support ◽  
Step Process ◽  
Resource Pooling ◽  
Organizational Information ◽  
The Common ◽  
Business To Business ◽  
New Framework

This paper aims at developing a framework for business-to-business (B2B) inter-organizational systems (IOSs), based on real-world IOS examples. Based upon two dimensions, role linkage and system support level, we propose a new framework that classifies IOSs into four basic types: (1) resource pooling, (2) operational cooperation, (3) operational coordination, and (4) complementary cooperation. We review select cases that fit into each category and consider the common characteristics of systems in each category. Then we draw implications for IOS planning and suggest a five-step process for creating an IOS plan. It is argued that each category of IOS needs to be linked with a specific business strategy, although each employs a common technical infrastructure.

NEW FICTITIOUS DOMAIN METHODS: FORMULATION AND ANALYSIS

2005 ◽  
Vol 15 (10) ◽  
pp. 1575-1594 ◽  
Author(s):  
IVO BABUŠKA ◽  
EUGENE G. PODNOS ◽  
GREGORY J. RODIN
Keyword(s):  
Model Problem ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Fictitious Domain ◽  
Element Mesh ◽  
Multiple Interfaces ◽  
Fictitious Domain Methods ◽  
The Cost

Two closely-related fictitious domain methods for solving problems involving multiple interfaces are introduced. Like other fictitious domain methods, the proposed methods simplify the task of finite element mesh generation and provide access to solvers that can take advantage of uniform structured grids. The proposed methods do not involve the Lagrange multipliers, which makes them quite different from existing fictitious domain methods. This difference leads to an advantageous form of the inf–sup condition, and allows one to avoid time-consuming integration over curvilinear surfaces. In principle, the proposed methods have the same rate of convergence as existing fictitious domain methods. Nevertheless it is shown that, at the cost of introducing additional unknowns, one can improve the quality of the solution near the interfaces. The methods are presented using a two-dimensional model problem formulated in the context of linearized theory of elasticity. The model problem is sufficient for presenting method details and mathematical foundations. Although the model problem is formulated in two dimensions and involves only one interface, there are no apparent conceptual difficulties to extending the methods to three dimensions and multiple interfaces. Further, it is possible to extend the methods to nonlinear problems involving multiple interfaces.

scholarly journals NEW DISCRETE STATES IN TWO-DIMENSIONAL SUPERGRAVITY

2007 ◽  
Vol 22 (07) ◽  
pp. 1375-1394 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Operator Algebra ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Field Theories ◽  
Two Dimensional ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving ◽  
Volume Preserving ◽  
Lowering Operator

Two-dimensional string theory is known to contain the set of discrete states that are the SU (2) multiplets generated by the lowering operator of the SU (2) current algebra. Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. In this paper we show that the interaction of d = 2 superstrings with the superconformal β - γ ghosts enlarges the actual algebra of the dimension 1 currents and hence the new ghost-dependent discrete states appear. Generally, these states are the SU (N) multiplets if the algebra includes the currents of ghost numbers n : -N ≤ n ≤ N - 2, not related by picture changing. We compute the structure constants of these ghost-dependent discrete states for N = 3 and express them in terms of SU (3) Clebsch–Gordan coefficients, relating this operator algebra to the volume preserving diffeomorphisms in d = 3. For general N, the operator algebra is conjectured to be isomorphic to SDiff (N). This points at possible holographic relations between two-dimensional superstrings and field theories in higher dimensions.

Critical intensities of Boolean models with different underlying convex shapes

2002 ◽  
Vol 34 (01) ◽  
pp. 48-57
Author(s):  
Rahul Roy ◽  
Hideki Tanemura
Keyword(s):  
Unit Area ◽  
Higher Dimensions ◽  
Boolean Model ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Boolean Models ◽  
Regular Polytope ◽  
Minimum Value ◽  
Critical Intensity ◽  
Poisson Boolean Model

We consider the Poisson Boolean model of percolation where the percolating shapes are convex regions. By an enhancement argument we strengthen a result of Jonasson (2000) to show that the critical intensity of percolation in two dimensions is minimized among the class of convex shapes of unit area when the percolating shapes are triangles, and, for any other shape, the critical intensity is strictly larger than this minimum value. We also obtain a partial generalization to higher dimensions. In particular, for three dimensions, the critical intensity of percolation is minimized among the class of regular polytopes of unit volume when the percolating shapes are tetrahedrons. Moreover, for any other regular polytope, the critical intensity is strictly larger than this minimum value.

Asymptotic properties of the equilibrium probability of identity in a geographically structured population

1977 ◽  
Vol 9 (2) ◽  
pp. 268-282 ◽  
Author(s):  
Stanley Sawyer
Keyword(s):  
Nearest Neighbor ◽  
Asymptotic Properties ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Order Zero ◽  
Structured Population ◽  
Equilibrium Probability ◽  
Migration Law

Let I(x, u) be the probability that two genes found a vector distance x apart are the same type in an infinite-allele selectively-neutral migration model with mutation rate u. The creatures involved inhabit an infinite of colonies, are diploid and are held at N per colony. Set in one dimension and in higher dimensions, where σ2 is the covariance matrix of the migration law (which is assumed to have finite fifth moments). Then in one dimension, in two dimensions, and in three dimensions uniformly for Here C0 is a constant depending on the migration law, K0(y) is the Bessel function of the second kind of order zero, and are the eigenvalues of σ2. For symmetric nearest-neighbor migrations, in one dimension and log mi in two. For is known in one dimension and C0 does not appear. In two dimensions, These results extend and make more precise earlier work of Malécot, Weiss and Kimura and Nagylaki.

Multicomponent Energy Conserving Dissipative Particle Dynamics: A General Framework for Mesoscopic Heat Transfer Applications

2008 ◽  
Author(s):  
Anuj Chaudhri ◽  
Jennifer R. Lukes
Keyword(s):  
Dissipative Particle Dynamics ◽  
Multicomponent System ◽  
Particle Dynamics ◽  
Two Dimensions ◽  
Scaling Factors ◽  
Dimensionless Groups ◽  
Energy Conserving ◽  
Steady State Heat ◽  
New Framework ◽  
Transient And Steady State

The energy conserving formulation of the Dissipative Particle Dynamics (DPD) mesoscale method for multicomponent systems is analyzed thoroughly. A new framework is established by identifying the dimensionless groups using general scaling factors. When the scaling factors are chosen based on the solvent in a multicomponent system, the reduced system of equations can easily be solved computationally. Simulation results are presented for one dimensional transient and steady-state heat conduction in a random DPD solid, which compare well with existing published and analytical solutions. This model is extended to two dimensions and shows excellent agreement with the analytical solution.

scholarly journals AdS3/AdS2 degression of massless particles

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Konstantin Alkalaev ◽  
Alexander Yan
Keyword(s):  
Massless Particle ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Spin Representation ◽  
Theoretical Terms ◽  
Finite Spectrum ◽  
Branching Rules ◽  
Higher Spin ◽  
Massless Fields ◽  
Kaluza Klein

Abstract We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS3 space foliated into AdS2 hypersurfaces. It is shown that an AdS3 massless particle of spin s = 1, 2, …, ∞ degresses into a couple of AdS2 particles of equal energies E = s. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS3/AdS2 degression we consider branching rules for AdS3 isometry algebra o(2,2) representations decomposed with respect to AdS2 isometry algebra o(1,2). We find that a given o(2,2) higher-spin representation lying on the unitary bound (i.e. massless) decomposes into two equal o(1,2) modules. In the field-theoretical terms, this phenomenon is demonstrated for spin-2 and spin-3 free massless fields. The truncation to a finite spectrum can be seen by using particular mode expansions, (partial) diagonalizations, and identities specific to two dimensions.

scholarly journals Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3000
Author(s):  
Eric T. Chung ◽  
Yalchin Efendiev ◽  
Wing Tat Leung ◽  
Wenyuan Li
Keyword(s):  
Linear Equations ◽  
Nonlinear Problems ◽  
Time Discretization ◽  
Numerical Results ◽  
Explicit Methods ◽  
Implicit Methods ◽  
Time Step ◽  
Multiscale Problems ◽  
Time Stepping ◽  
Space Decomposition

This work continues a line of work on developing partially explicit methods for multiscale problems. In our previous works, we considered linear multiscale problems where the spatial heterogeneities are at the subgrid level and are not resolved. In these works, we have introduced contrast-independent, partially explicit time discretizations for linear equations. The contrast-independent, partially explicit time discretization divides the spatial space into two components: contrast dependent (fast) and contrast independent (slow) spaces defined via multiscale space decomposition. Following this decomposition, temporal splitting was proposed, which treats fast components implicitly and slow components explicitly. The space decomposition and temporal splitting are chosen such that they guarantees stability, and we formulated a condition for the time stepping. This condition was formulated as a condition on slow spaces. In this paper, we extend this approach to nonlinear problems. We propose a splitting approach and derive a condition that guarantees stability. This condition requires some type of contrast-independent spaces for slow components of the solution. We present numerical results and show that the proposed methods provide results similar to implicit methods with a time step that is independent of the contrast.

Sign in / Sign up

Export Citation Format

Share Document