## Efficient High-Order Operator Format

While a global (parallel) sparse matrix is a good representation of a PDE operator discretized with low-order elements, a global parallel matrix is a poor choice when discretizing with high-order elements, due to the large cost of both the memory transfer and floating point operations.

CEED is developing an alternative operator format, based on the CEED low-level API, that allows efficient operator evaluation that is optimal in memory and nearly-optimal in FLOPs cost.

*This is an active area of research for our team and we are interested in
collaboration.*

*Stay tuned for more details...*

## General Interpolation of Solution Field Values

Particle tracking, grid-to-grid transfer and data analysis are typical operations that require off-grid function evaluation.

CEED is developing a scalable interpolation routine for arbitrary-order hexahedral elements that uses a hash table to rapidly identify candidate elements/processors that might contain the point in question, followed by a Newton iteration to find the point in the reference domain.

The iteration is based on minimization, rather than root-finding, which is advantageous when the interpolation point is on or near an element boundary where high-order interpolants tend to exhibit rapid variation.

*This is an active area of research for our team and we are interested in
collaboration.*

*Stay tuned for more details...*