Grid-based deterministic dose-calculation methods for radiotherapy planning require the use of six-dimensional phase space grids. Because of the large number of phase space dimensions, a growing number of medical physicists appear to believe that grid-based deterministic dose-calculation methods are not competitive with Monte Carlo methods. We argue that this conclusion may be premature. Our re...

The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by a diagnostic quantity called smoothing error. In this paper it is shown that, regardless of the usefulness of the smoothing error as a diagnostic tool in its own right, the concept of the smoothing error as a component of the retrieval error budget i...

The point-source traveltime field has an upwind singularity at the source point. Consequently, all formally high-order, finite-difference eikonal solvers exhibit firstorder convergence and relatively large errors. Adaptive upwind finite-difference methods based on high-order Weighted Essentially NonOscillatory (WENO) RungeKutta difference schemes for the paraxial eikonal equation overcome this ...

We describe a GPUand multicore-oriented implementation technique for a key component of finite element based simulation toolkits for partial differential equations on unstructured grids: Geometric Multigrid solvers. We use efficient sparse matrix-vector multiplications throughout the solver pipeline: within the coarse-grid solver, smoothers and even grid transfers. Our implementation can handle...

We present a finite difference scheme, applicable to general irregular planar domains, to approximate the biharmonic equation. The irregular domain is embedded in a Cartesian grid. In order to approximate ∆Φ at a grid point we interpolate the data on the (irregular) stencil by a polynomial of degree six. The finite difference scheme is ∆2QΦ(0, 0), where QΦ is the interpolation polynomial. The i...