scholarly journals ParallelN-Body Simulation Based on the PM and P3M Methods Using Multigrid Schemes in conjunction with Generic Approximate Sparse Inverses

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
P. E. Kyziropoulos ◽  
C. K. Filelis-Papadopoulos ◽  
G. A. Gravvanis
Keyword(s):  
Linear Systems ◽  
Nodal Point ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Gravity Potential ◽  
Time Step ◽  
Multigrid Algorithm ◽  
Simulation Based ◽  
Mesh Method ◽  
Large Linear Systems

During the last decades, Multigrid methods have been extensively used for solving large sparse linear systems. Considering their efficiency and the convergence behavior, Multigrid methods are used in many scientific fields as solvers or preconditioners. Herewith, we propose two hybrid parallel algorithms forN-Body simulations using the Particle Mesh method and the Particle Particle Particle Mesh method, respectively, based on the V-Cycle Multigrid method in conjunction with Generic Approximate Sparse Inverses. TheN-Body problem resides in a three-dimensional torus space, and the bodies are subject only to gravitational forces. In each time step of the above methods, a large sparse linear system is solved to compute the gravity potential at each nodal point in order to interpolate the solution to each body. Then the Velocity Verlet method is used to compute the new position and velocity from the acceleration of each respective body. Moreover, a parallel Multigrid algorithm, with a truncated approach in the levels computed in parallel, is proposed for solving large linear systems. Furthermore, parallel results are provided indicating the efficiency of the proposed MultigridN-Body scheme. Theoretical estimates for the complexity of the proposed simulation schemes are provided.

scholarly journals Direct Verification of Linear Systems with over 10000 Dimensions

10.29007/dwj1 ◽  
2018 ◽  
Author(s):  
Stanley Bak ◽  
Parasara Sridhar Duggirala
Keyword(s):  
Linear Systems ◽  
Computation Time ◽  
Order Reduction ◽  
Direct Analysis ◽  
Principle Of Superposition ◽  
Basis Matrix ◽  
Time Step ◽  
Model Order ◽  
Large Linear Systems ◽  
Core Part

We evaluate a recently-proposed reachability method on a set of high-dimensional lin- ear system benchmarks taken from model order reduction and presented in ARCH 2016. The approach uses a state-set representation called a generalized star set and the principle of superposition of linear systems to achieve scalability. The method was previously shown to have promise in terms of scalability for direct analysis of large linear systems. For each benchmark, we also compare computing the basis matrix, a core part of the reachabil- ity method, using numerical simulations versus a matrix exponential formulation. The approach successfully analyzes systems with hundreds of dimensions in minutes, and can scale to systems that have over 10000 dimensions with a computation time ranging from tens of minutes to tens of hours, depending on the desired time step.

scholarly journals The Influence of Mesh Resolution on 3D RANS Flow Simulations in Turbomachinery Flow Parts

2021 ◽  
Vol 24 (1) ◽  
pp. 13-27
Author(s):  
Serhii V. Yershov ◽  
◽  
Viktor A. Yakovlev ◽  
Keyword(s):  
General Structure ◽  
Complex Structure ◽  
Three Dimensional ◽  
Estimation Method ◽  
Second Order ◽  
Computational Domain ◽  
Time Step ◽  
Multigrid Algorithm ◽  
Grid Convergence ◽  
Number Of Cells

The question of the difference mesh refinement degree influence on the results of calculation of the three-dimensional viscous gas flows in the flow parts of turbomachines using the RANS flow models and second order numerical methods is considered. Calculations of flows for a number of turbine and compressor grids on successively refining grids have been performed. We used H-type grids with approximate orthogonalization of cells in the boundary layer. The calculations were carried out using a CFD solver F with the use of an implicit ENO scheme of the second order, a local time step, and a simplified multigrid algorithm. When calculating the flow on fine grids, the following were used: convergence acceleration tools implemented in the solver; truncation of the computational domain with subsequent distribution of the results based on the symmetry property; the computational domain splitting into parts and computations parallelizing. Comparison of the obtained results is carried out, both in terms of qualitative resolution of the complex structure of three-dimensional flows, and in terms of quantitative assessment of losses. Grid convergence was estimated in two ways. In the first, the characteristic two-dimensional distributions of parameters obtained on different grids were visually compared. The purpose of such comparisons was to evaluate the sufficient degree of solution of both the general structure of the flow in grids and its features, namely, shock waves, contact discontinuities, separation zones, wakes, etc. The second estimation method is based on the grid convergence index (GCI). The GCI calculated from the three-dimensional density field was considered in this paper. It is concluded that for scientific research requiring high accuracy of calculations and detailing of the structure of a three-dimensional flow, very fine difference meshes with the number of cells from 106 to 108 in one blade-to-blade channel are needed, while for engineering calculations, under certain conditions, it is sufficient to use meshes with the number of cells less than 1 million in one blade-to-blade channel.

scholarly journals Multigrid methods for block‐Toeplitz linear systems: convergence analysis and applications

2020 ◽  
Author(s):  
Marco Donatelli ◽  
Paola Ferrari ◽  
Isabella Furci ◽  
Stefano Serra‐Capizzano ◽  
Debora Sesana
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Multigrid Methods

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

Forklift Hydraulic System Simulation Based on ADAMS

2012 ◽  
Vol 424-425 ◽  
pp. 598-602 ◽  
Author(s):  
You Min Wang ◽  
Chun Zhao ◽  
Jian Hua Zhang
Keyword(s):  
Hydraulic System ◽  
Production Cost ◽  
Control Function ◽  
Three Dimensional ◽  
Improve Design ◽  
Kinematics Simulation ◽  
Simulation Based ◽  
Motion Speed ◽  
Work Size ◽  
Control Functional

In order to improve design performance, shorten development cycles, reduce production cost, we design and research the forklift hydraulic system, developed forklift hydraulic system diagram. Forklift virtual prototype’s 3-D solid modeling is designed by Pro / E three-dimensional software, and imported into the ADAMS environment. Add constraints and drivers exert the control function separately to the tilting cylinder and lifting cylinder, carry on the kinematics simulation. Through the analysis to the compound motion actuation control functional arrangement、the compound motion speed graph、the gate’s tilt angle graph、the tilting cylinder stress graph and the lifting cylinder stress graph, he simulation result indicated: each cylinder design is reasonable, the movement without interference，the reasonable work scope satisfied to the work size request

Simulation on Torpedo Unsteady Hydrodynamic with the Movement in the Longitudinal Plane

2013 ◽  
Vol 791-793 ◽  
pp. 1073-1076
Author(s):  
Ming Yang ◽  
Shi Ping Zhao ◽  
Han Ping Wang ◽  
Lin Peng Wang ◽  
Shao Zhu Wang
Keyword(s):  
Three Dimensional ◽  
Engineering Application ◽  
Calculation Model ◽  
Trajectory Design ◽  
Design Calculation ◽  
Variable Speed ◽  
Accurate Calculation ◽  
Longitudinal Plane ◽  
Submerged Body ◽  
Mesh Method

The unsteady hydrodynamic accurate calculation is the premise of submerged body trajectory design and maneuverability design. Calculation model of submerged body unsteady hydrodynamic with the movement in the longitudinal plane was established, which based on unsteady three-dimensional incompressible fluid dynamics theory. Variable speed translational and variable angular velocity of the pitching motion in the longitudinal plane of submerged body was achieved by dynamic mesh method. The unsteady hydrodynamic could be obtained by model under the premise of good quality grid by the results. Modeling methods can learn from other similar problems, which has engineering application value.

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

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