At this point, we argue that reliability, performance and accuracy considerations will again reach the forefront.
In so doing, the generic OBR formulation separates accuracy considerations from the enforcement of physical properties.
In so doing, we separate accuracy considerations, handled by the objective functional, from the enforcement of physical bounds, handled by the constraints.
Remapping has many advantages, not the least of which is that the time step is limited only by accuracy considerations, but it tends to be expensive and complex.
Concerns regarding performance measures include technical concerns (eg, validity, risk adjustment, sample size, and accuracy considerations), concerns regarding the cost of implementation, and concerns regarding unintended consequences.
Such coupling needs arise when either specific solution methods or accuracy considerations necessitate that different and disjoint subdomains be treated with different (Eulerian or Lagrangian) schemes.
The point is that, piece by piece, the principles that are taken to govern the degree of support provided to a proposition by a body of evidence are being shown to follow from accuracy considerations alone.
An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation.
In this multi-scale method, the plasma particles in each region of phase space are advanced using a step size appropriate to that region, as determined by accuracy considerations.
Analysis of the linear stability of the scheme reveals that the Courant–Friedrichs Lewy condition on the time step associated with gravity and acoustic waves can be circumvented and the maximum stable time step can be brought into closer agreement with the time step limitations arising from accuracy considerations.
