Language: C++

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The LJJ-CVV-MPI program implements the construction of the current-voltage characteristic in a system of long Josephson junctions with inductive and capacitive coupling. The program is written in the C++ programming language and using MPI parallel programming technology.

The LJJ system is described by the following initial boundary value problem:

,              (1)

where - inductive coupling matrix.

Here x = [0,L] is the coordinate along the contact length, t = [0,T] is time, φ_l(x,t) and V_l(x,t) are the desired functions, respectively, of the phase difference and voltage in the l-th JJ stack (l = 1,...,N), β = σV₀ / (d_Ij_c) – dissipation parameter, S – inductive coupling parameter, which takes values in the interval 0 < |S| < 0.5. D_c is the effective electrical thickness of the JJ, normalized to the thickness of the dielectric layer. s_c – capacitive coupling parameter, I – external current. All quantities in system (1) are converted to dimensionless.

Boundary conditions:

Initial conditions at the beginning of counting at I = 0: φ_l(x,0) = V_l(x,0) = 0. Further, with increasing external current, for each next value of I, the initial conditions are the solutions obtained for the previous value of I at t = T.

To numerically solve system (1), a uniform discrete coordinate grid is introduced and a finite-difference formula of second order accuracy is used to approximate the derivatives. Thus, we obtain the Cauchy problem regarding the desired functions at the nodes of the discrete grid. This problem is solved using the 4-step Runge Kutta method.

The calculation of the current-voltage characteristic is reduced to repeatedly solving problem (1) with a sequential increase in the value and then a decrease in the external current parameter. Voltage values are averaged over the length of the contact, over all contacts and over a specified time interval. The mathematical formulation of the problem, the method of numerical solution and the features of parallel implementation are described in more detail in [1].

To run the program, you need to compile the source code file (Intel compiler is recommended) and run the script_mpi.sh script. In the script, after the program launch command (mpirun), you must specify the launch parameters separated by a space in a clear order (number_of_contacts length_of_contacts inductive_coupling_parameter capacitive_coupling_parameter). The remaining parameters are changed in the source code file.

Detailed description of the launch procedure and an explanation of a specific example of launching a program is given in the readme file. The archive includes, in addition to this file, a program in MPI-C++, a script for launching the program, as well as the result of running the program with specific input parameters.

Sources with readme, script as well as the result of running the program with specific input parameters.

References:

1. 1. M. V. Bashashin, E. V. Zemlyanaya, I. R. Rahmonov, Yu. M. Shukrinov, P. Kh. Atanasova, A. V. Volokhova. Numerical approach and parallel implementation for computer simulation of stacked long Josephson Junctions. Computer Research and Modeling, 2016, vol.8, no.4, pp.593–604.

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