scholarly journals MagIC v5.10: a two-dimensional MPI distribution for pseudo-spectral magneto hydrodynamics simulations in spherical geometry

2021 ◽  
Author(s):  
Rafael Lago ◽  
Thomas Gastine ◽  
Tilman Dannert ◽  
Markus Rampp ◽  
Johannes Wicht
Keyword(s):  
High Performance ◽  
Spherical Geometry ◽  
Distribution Data ◽  
Two Dimensional ◽  
Data Layout ◽  
Time Step ◽  
One Dimensional ◽  
Dimensional Distribution ◽  
Grid Points ◽  
Pseudo Spectral

Abstract. We discuss two parallelization schemes for MagIC, an open-source, high-performance, pseudo-spectral code for the numerical solution of the magneto hydrodynamics equations in a rotating spherical shell. MagIC calculates the non-linear terms on a numerical grid in spherical coordinates while the time step updates are performed on radial grid points with a spherical harmonic representation of the lateral directions. Several transforms are required to switch between the different representations. The established hybrid implementation of MagIC uses MPI-parallelization in radius and relies on existing fast spherical transforms using OpenMP. Our new two-dimensional MPI decomposition implementation also distributes the latitudes or the azimuthal wavenumbers across the available MPI tasks/compute cores. We discuss several non-trivial algorithmic optimizations and the different data distribution layouts employed by our scheme. In particular, the two-dimensional distribution data layout yields a code that strongly scales well beyond the limit of the current one-dimensional distribution. We also show that the two-dimensional distribution implementation, although not yet fully optimized, can already be faster than the existing finely optimized hybrid implementation when using many thousands of CPU cores. Our analysis indicates that the two-dimensional distribution variant can be further optimized to also surpass the performance of the one-dimensional distribution for a few thousand cores.

scholarly journals MagIC v5.10: a two-dimensional message-passing interface (MPI) distribution for pseudo-spectral magnetohydrodynamics simulations in spherical geometry

2021 ◽  
Vol 14 (12) ◽  
pp. 7477-7495
Author(s):  
Rafael Lago ◽  
Thomas Gastine ◽  
Tilman Dannert ◽  
Markus Rampp ◽  
Johannes Wicht
Keyword(s):  
Message Passing ◽  
Message Passing Interface ◽  
Distribution Data ◽  
Two Dimensional ◽  
Data Layout ◽  
Time Step ◽  
One Dimensional ◽  
Hybrid Parallelization ◽  
Dimensional Distribution ◽  
Pseudo Spectral

Abstract. We discuss two parallelization schemes for MagIC, an open-source, high-performance, pseudo-spectral code for the numerical solution of the magnetohydrodynamics equations in a rotating spherical shell. MagIC calculates the non-linear terms on a numerical grid in spherical coordinates, while the time step updates are performed on radial grid points with a spherical harmonic representation of the lateral directions. Several transforms are required to switch between the different representations. The established hybrid parallelization of MagIC uses message-passing interface (MPI) distribution in radius and relies on existing fast spherical transforms using OpenMP. Our new two-dimensional MPI decomposition implementation also distributes the latitudes or the azimuthal wavenumbers across the available MPI tasks and compute cores. We discuss several non-trivial algorithmic optimizations and the different data distribution layouts employed by our scheme. In particular, the two-dimensional distribution data layout yields a code that strongly scales well beyond the limit of the current one-dimensional distribution. We also show that the two-dimensional distribution implementation, although not yet fully optimized, can already be faster than the existing finely optimized hybrid parallelization when using many thousands of CPU cores. Our analysis indicates that the two-dimensional distribution variant can be further optimized to also surpass the performance of the one-dimensional distribution for a few thousand cores.

scholarly journals High performance self-powered photodetector based on 1D Te-2D WS2 mixed-dimensional heterostructure

2021 ◽  
Author(s):  
Lixiang Han ◽  
Mengmeng Yang ◽  
Peiting Wen ◽  
Wei Gao ◽  
nengjie huo ◽  
...  
Keyword(s):  
High Performance ◽  
Van Der Waals ◽  
Sharp Interface ◽  
Two Dimensional ◽  
High Quality ◽  
One Dimensional ◽  
Self Powered

One dimensional (1D)-two dimensional (2D) van der Waals (vdWs) mixed-dimensional heterostructures with advantages of atomically sharp interface, high quality and good compatibility have attracted tremendous attention in recent years. The...

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

scholarly journals Two-Dimensional-One-Dimensional Alternating Direction Schemes for Coastal Systems Convection-Diffusion Problems

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3267
Author(s):  
Alexander Sukhinov ◽  
Valentina Sidoryakina
Keyword(s):  
Information Exchange ◽  
Problem Solution ◽  
Two Dimensional ◽  
Splitting Scheme ◽  
Time Step ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Coastal Systems ◽  
Alternating Direction ◽  
Matter Transport

The initial boundary value problem for the 3D convection-diffusion equation corresponding to the mathematical model of suspended matter transport in coastal marine systems and extended shallow water bodies is considered. Convective and diffusive transport operators in horizontal and vertical directions for this type of problem have significantly different physical and spectral properties. In connection with the above, a two-dimensional–one-dimensional splitting scheme has been built—a three-dimensional analog of the Peaceman–Rachford alternating direction scheme, which is suitable for the operational suspension spread prediction in coastal systems. The paper has proved the theorem of stability solution with respect to the initial data and functions of the right side, in the case of time-independent operators in special energy norms determined by one of the splitting scheme operators. The accuracy has been investigated, which, as in the case of the Peaceman–Rachford scheme, with the special definition of boundary conditions on a fractional time step, is the value of the second order in dependency of time and spatial steps. The use of this approach makes it possible to obtain parallel algorithms for solving grid convection-diffusion equations which are economical in the sense of total time of problem solution on multiprocessor systems, which includes time for arithmetic operations realization and the one required to carry of information exchange between processors.

High-Performance and Ultralow-Noise Two-Dimensional Heterostructure Field-Effect Transistors with One-Dimensional Electrical Contacts

2021 ◽  
Vol 3 (9) ◽  
pp. 4126-4134
Author(s):  
Aroop K. Behera ◽  
Charles Thomas Harris ◽  
Douglas V. Pete ◽  
Collin J. Delker ◽  
Per Erik Vullum ◽  
...  
Keyword(s):  
Field Effect ◽  
High Performance ◽  
Field Effect Transistors ◽  
Electrical Contacts ◽  
Two Dimensional ◽  
One Dimensional ◽  
Heterostructure Field Effect Transistors

scholarly journals The Maximum of a Symmetric Next Neighbor Walk on the Nonnegative Integers

2014 ◽  
Vol 51 (01) ◽  
pp. 162-173
Author(s):  
Ora E. Percus ◽  
Jerome K. Percus
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
Generating Functions ◽  
Two Dimensional ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Dimensional Distribution

We consider a one-dimensional discrete symmetric random walk with a reflecting boundary at the origin. Generating functions are found for the two-dimensional probability distribution P{S n = x, max1≤j≤n S n = a} of being at position x after n steps, while the maximal location that the walker has achieved during these n steps is a. We also obtain the familiar (marginal) one-dimensional distribution for S n = x, but more importantly that for max1≤j≤n S j = a asymptotically at fixed a 2 / n. We are able to compute and compare the expectations and variances of the two one-dimensional distributions, finding that they have qualitatively similar forms, but differ quantitatively in the anticipated fashion.

Calibration of a 1D/1D urban flood model using 1D/2D model results in the absence of field data

2011 ◽  
Vol 64 (5) ◽  
pp. 1016-1024 ◽  
Author(s):  
J. Leandro ◽  
S. Djordjević ◽  
A. S. Chen ◽  
D. A. Savić ◽  
M. Stanić
Keyword(s):  
Field Data ◽  
Computational Time ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Time Step ◽  
Urban Flood ◽  
One Dimensional ◽  
1D Model ◽  
Surface Network ◽  
2D Model

Recently increased flood events have been prompting researchers to improve existing coupled flood-models such as one-dimensional (1D)/1D and 1D/two-dimensional (2D) models. While 1D/1D models simulate sewer and surface networks using a one-dimensional approach, 1D/2D models represent the surface network by a two-dimensional surface grid. However their application raises two issues to urban flood modellers: (1) stormwater systems planning/emergency or risk analysis demands for fast models, and the 1D/2D computational time is prohibitive, (2) and the recognized lack of field data (e.g. Hunter et al. (2008)) causes difficulties for the calibration/validation of 1D/1D models. In this paper we propose to overcome these issues by calibrating a 1D/1D model with the results of a 1D/2D model. The flood-inundation results show that: (1) 1D/2D results can be used to calibrate faster 1D/1D models, (2) the 1D/1D model is able to map the 1D/2D flood maximum extent well, and the flooding limits satisfactorily in each time-step, (3) the 1D/1D model major differences are the instantaneous flow propagation and overestimation of the flood-depths within surface-ponds, (4) the agreement in the volume surcharged by both models is a necessary condition for the 1D surface-network validation and (5) the agreement of the manholes discharge shapes measures the fitness of the calibrated 1D surface-network.

Coupling of One-Dimensional and Two-Dimensional Hydrodynamic Models Using an Immersed-Boundary Method

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Ning Zhang ◽  
Puxuan Li ◽  
Anpeng He
Keyword(s):  
Water Levels ◽  
Immersed Boundary ◽  
Two Dimensional ◽  
Hydrodynamic Models ◽  
One Dimensional ◽  
Flooding Event ◽  
Type Coupling ◽  
Grid Points ◽  
Flooding Events ◽  
Dry Cell

Numerical simulations of flooding events through rivers and channels require coupling between one-dimensional (1D) and two-dimensional (2D) hydrodynamic models. The rivers and channels are relatively narrow, and the widths could be smaller than the grid size used in the background 2D model. The shapes of the rivers and channels are often complex and do not necessarily coincide with the grid points. The coupling between the 1D and 2D models are challenging. In this paper, a novel immersed-boundary (IB) type coupling is implemented. Using this method, no predetermined linking point is required, nor are the discharge boundary conditions needed to be specified on the linking points. The linkage will be dynamically determined by comparing the water levels in the 1D channel and the surrounding dry cell elevations on the 2D background. The linking-point flow conditions, thus, can be dynamically calculated by the IB type implementation. A typical problem of the IB treatment, which is the forming of the nonsmooth zigzag shaped boundary, has not been observed with this method. This coupling method enables more realistic and accurate simulations of water exchange between channels and dry lands during a flooding event.

scholarly journals 51. Interpretation of solar radio-frequency disk brightness distributions derived from observations with aerials extended in one dimension

1957 ◽  
Vol 4 ◽  
pp. 290-293 ◽  
Author(s):  
S. F. Smerd ◽  
J. P. Wild
Keyword(s):  
Solar Radio ◽  
Synthesis Method ◽  
One Dimension ◽  
Solar Model ◽  
Two Dimensional ◽  
Fourier Synthesis ◽  
One Dimensional ◽  
Finite Resolution ◽  
Dimensional Distribution ◽  
The Individual

Several recent papers have dealt with observations of brightness distributions over the solar disk, which were derived either from two-aerial interferometer observations at various spacings and orientations (e.g. O'Brien, 1953) [1], or from multiple-element interferometer fan-beam observations at various orientations (e.g. Christiansen and Warburton, 1954) [2], In each a two-dimensional distribution is derived from a number of essentially one-dimensional observations by a Fourier synthesis method described by O'Brien. The detail given by these methods must be limited by the finite resolution of the individual observations (limited by the maximum aperture of the aerial system), but the form of the limitation is not obvious, though its knowledge is required when relating the observations to a solar model.

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