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Therefore, we established the injection wellbore constraint equations, which were coupled with the oil/water two-phase numerical reservoir models, and then the seven diagonal form sparse coefficient matrix was solved by block precondition of generalized minimal residual algorithm.
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The global stiffness matrix is solved using Gauss elimination method.
Note that the matrix is solved in (a).
By minimizing in (11), the MMSE MIMO LE matrix is solved as (12).
The case of immeasurable state is considered where the observer gain matrix is solved by Sylvester equation.
In this approach, the fracture pressure and water saturations in fracture and the matrix pressure and water saturation in matrix are solved iteratively.
In this case, the problem of how to construct the Cauchy matrix is solved analytically thanks to a delayed matrix exponential, as defined below.
The problem, written in primal formulation on both the fractures and the porous matrix, is solved resorting to the constrained minimization of a properly designed cost functional that expresses the matching conditions at fracture fracture and fracture matrix interfaces.
The fracture network, treated as planar sinks and sources embedded in the matrix, is solved via the boundary element method and the flow within the fracture networks is unidirectional and it is solved via the finite element method.
Since the beam is not divided at the damage location, rather than an 8 by 8, only a 4 by 4 matrix is solved to obtain the natural frequencies and mode shapes.
60 Once the transformation matrix is solved, the delineated lesion can be transferred to the registered IR image.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com