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The variable ( z_{gj}^ ) is the value of global solution variable j in a current epoch.
For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes.
Furthermore, the first and second order schemes are shown to achieve one order higher accuracy for the solution variable in the advection limit.
The multiple-affinity model builds the relationship model among main entities and concepts in multiobjective problems (MOPs) and multiobjective evolutionary algorithms (MOEAs), including feasible solution, variable space, objective space, Pareto-optimal set, ranking and crowding distance.
To this end, we propose a new strategy to perform the coarse grid correction so that the auxiliary variables and the solution variable are corrected separately in a mixed pattern.
The primary solution variable(s) is/are assumed to take the form of a truncated Taylor series around a point c, and the unknown coefficients of the expansion are determined using the governing differential equation(s) and boundary conditions.
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Velocity u, density ρ, viscosity μ and other solution variables represent ensemble-averaged (or time-averaged) values.
Fiber quality was optimized by manipulating the process and solution variables to fabricate continuous bead-free fibers.
Alternative formulations for structural optimization are also described where the design and the analysis variables are treated as solution variables simultaneously.
In parallel, over forty finite element simulations were performed, examining a wide range of solution variables and their impact on the predicted residual stresses.
The obtained sensitivity expression, which can be computed by simple algebraic manipulation of the solution variables, is well suited for numerical implementation and provides accurate values.
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