The weak form of the grid equations is solved using the finite element approximation, which reduces the grid equations to a nonlinear, algebraic set.
Doing it in the same way with other of Maxwell's equations and using Ampère's law in the case of a dual grid, allows a complete discretised set of Maxwell's grid equations (MGEs) to be obtained.
Using the Maxwell-grid-equations (MGEs) of the finite integration technique, a geometric discretization scheme for Maxwell's equations, this new approach has been implemented in a parallel environment in order to account for the memory-demanding high-resolution anatomy models used for the calculation of induced currents inside the human body.
The coarse-grid equations are derived by averaging of the multigroup diffusion equations over energy.
The singular part is defined to be the region Ω S = { ( x, y ) : − 1 2 ≤ x ≤ 1 2, − 3 4 ≤ y ≤ 3 4 } ∖ Ω 1 s, where Ω 1 s = { ( x, y ) : 0 ≤ x ≤ 1 2, − 3 4 ≤ y ≤ 0 }, and the nonsingular part is Ω N S = Ω / Ω S. The system of Block-Grid equations is solved by Schwarz's alternating method.
For the solution of the block-grid equations, Schwarz's alternating method is used.
It is also shown that for a sufficiently fine grid, the differential equations of the pivots could be decoupled from that of the discrete number density allowing a sequential solution in time.
To analyze the steady-state flow in the gas grid, the nodal balance equations of the system are presented firstly.
The wave propagation in each grid point was calculated by solving equations of motions using a staggered-grid FDM with fourth-order and second-order in space and time, respectively.
All of the oil water residual equations of reservoir grids are combined as a huge linear equation set (Eq. 9), which can also be written as the matrix formats with seven diagonal sparse coefficient matrix, and its structure is as same as the coefficient matrix of conventional reservoir numerical simulation model without LSWI (Jigen et al. 2007).
