Sentence examples for underlying solution of the from inspiring English sources

The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation.

Despite the underlying simplifications, solution of the full CMC equations allows a single model to be used for the autoignition, flame propagation ("premixed mode"), and diffusion flame mode of diesel combustion, which makes CMC a good candidate model for practical engine calculations.

The choice of the local boundary conditions for the multi-sale basis functions determines the accuracy of the MsFEM numerical solution, and one needs to incorporate the global information of the elliptic equation into the local boundary conditions of the multi-scale basis functions to recover the underlying fine-mesh solution of the equation.

The abilities to respond in terms of certain relationships between stimuli, to abstract those relationships and invariant features from a complex and changing array of stimuli, and, above all perhaps, to transfer such learning to a completely novel set of physical stimuli seem to be some of the more important processes underlying the solution of complex discriminative problems.

We introduce an hp-adaptive finite element algorithm based on a combination of reliable and efficient residual error indicators and a new hp-extension control technique which assesses the local regularity of the underlying analytical solution on the basis of its local Legendre series expansion.

(1a)–(1g) to reveal the presence of different timescales; determine how to group timescales that are present; implement geometric singular perturbation theory (GSPT) to set up reduced systems based on separation of timescales; and use the reduced systems to explain the mechanisms underlying the dynamics of the SB solutions.

The current work addresses this problem by incorporating the underlying wave behaviour of the solution into the formulation of a boundary element, using ideas arising from the Partition of Unity finite element methods.

The solution of the underlying PDE, which describes magnetostatics, is represented using the generalized polynomial chaos expansion.