Innovation diffusion: A deterministic model of space-time integration with physical analog

In this paper, we develop a formalism based on either spatially or temporally integrated electromagnetic (EM) Lagrangian, which provides new insights about the near-field reactive energy around generic antennas for arbitrary spatio-temporal excitation signals. Using electric and magnetic fields calculated via FDTD technique and interpolation routines, we compute and plot the normalized values of space/time integrated EM Lagrangian around antennas. While the time-integration of EM Lagrangian sheds light onto the spatial distribution of inductive/capacitive reactive energy, time-variation of spatially integrated EM Lagrangian can help in design of ultra-wideband (UWB) MIMO antennas with low mutual coupling. The EM Lagrangian approach can assist in design of energy harvesting and wireless power transfer systems, as well as for electromagnetic interference mitigation applications.

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A Space-Time Parallel Method to Solve Space-Dependent Neutron Kinetics Equations in Hexagonal-Z Geometry

Volume 3: Nuclear Fuel and Material, Reactor Physics, and Transport Theory ◽

10.1115/icone26-81213 ◽

2018 ◽

Author(s):

Zhizhu Zhang ◽

Yun Cai ◽

Xingjie Peng ◽

Qing Li

Keyword(s):

Nuclear Reactor ◽

Time Integration ◽

Euler Method ◽

Space Time ◽

Parallel Method ◽

Sequential Method ◽

Neutron Kinetics ◽

Nodal Method ◽

Backward Euler ◽

Parareal Method

Neutron kinetics plays an important role in reactor safety and analysis. The backward Euler method is the most widely used time integration method in the calculation of space-dependent nuclear reactor kinetics. Diagonally Implicit Runge-Kutta (DIRK) method owns high accuracy and excellent stability and it could be applied to the neutron kinetics for hexagonal-z geometry application. As solving the neutron kinetics equations is very time-consuming and the number of available cores continues to increase with parallel architectures evolving, parallel algorithms need to be designed to utilize the available resources effectively. However, it is difficult to parallel in time axis since the later moment is strongly dependent on the previous moment. In this paper, the Parareal method which is a time parallel method and implemented by MPI in the processor level is studied in the hexagonal-z geometry with the help of DIRK method. In order to make good use of the parallelism, a parallel strategy in the space direction is also used. In the coarse nodal method, many same operations are finished in the nodes and these operations could be parallel by OpenMP in the thread level since they are independent. Several transient cases are used to validate this method. The results show that the Parareal method gets a fast-convergent speed such as only 2∼3 iterations are needed to convergent. This space-time parallel method could reduce the cost time compared to the sequential method.

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Improving El Niño prediction using a space-time integration of Indo-Pacific winds and equatorial Pacific upper ocean heat content

Geophysical Research Letters ◽

10.1029/2002gl016673 ◽

2003 ◽

Vol 30 (7) ◽

Cited By ~ 71

Author(s):

Allan J. Clarke ◽

Stephen Van Gorder

Keyword(s):

El Niño ◽

El Nino ◽

Time Integration ◽

Heat Content ◽

Space Time ◽

Equatorial Pacific ◽

Ocean Heat Content ◽

Upper Ocean ◽

Upper Ocean Heat Content

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Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method

Water ◽

10.3390/w12123580 ◽

2020 ◽

Vol 12 (12) ◽

pp. 3580

Author(s):

Cheng-Yu Ku ◽

Li-Dan Hong ◽

Chih-Yu Liu

Keyword(s):

Inverse Problems ◽

Boundary Conditions ◽

Numerical Solutions ◽

Separation Of Variables ◽

Time Integration ◽

Meshfree Method ◽

Space Time ◽

Basis Functions ◽

Trefftz Method ◽

Dimensional Boundary

This paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due to the basis functions completely satisfying the equation to be solved, collocation points are placed on the space–time boundaries. Numerical solutions are approximated based on the superposition theorem. Accordingly, the initial and boundary conditions are both regarded as space–time boundary conditions. Forward and inverse examples are conducted to validate the proposed approach. Emphasis is placed on the two-dimensional boundary detection problem in which the nonlinearity is solved using the fictitious time integration method. Results demonstrate that approximations with high accuracy are acquired in which the boundary data on the absent boundary may be efficiently recovered even when inaccessible partial data are provided.

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