Preface: This is in response to the request of the ILC GDE for a discussion of the strengths of the VORPAL parallel EM framework for the computations needed for the ILC. As background, we note that there are two codes proposed for such work, the VORPAL framework, which can incorporate algorithms for arbitrary hexahedral meshes, and SLAC finite element suite (Omega3p, Tau3p, etc.) which work on unstructured meshes. Applicability of VORPAL to Electromagnetics Calculation Summary: Recent algorithm additions have made the VORPAL framework [1] well suited for complex electromagnetic calculations such as those needed for computational Grand Challenges like ILC cavity modeling. Those additions include embedded boundary methods and python-scripted geometry generation. These new capabilities augment the previously demonstrated features of VORPAL: fully self-consistent particle modeling, scalability to 1000s of processors, and modest memory requirements compared to global algorithms. Object-oriented design allows developers to quickly add new capability to VORPAL, for example perfect dispersion algorithms and implicit time-stepping algorithms. VORPAL is presently installed at and available to researchers at FNAL, LBNL, JLAB, BNL, and ANL. The VORPAL framework computes the evolution for partial differential equations on a hexahedral mesh. It is a general framework that allows for particles, fields, and their interactions. Of most interest here is the finite-difference (FD), time-domain (TD) electromagnetics including particle effects through the Particle-In-Cell methods thus allowing the computation of the propagation of beams fully self-consistently. That is, particles respond to both the electromagnetic fields powered by the klystrons as well as those produced by the beam particles. VORPAL has had great success in the laser-wake-field research, and it now has demonstrated capability to handle complex boundary conditions needed for the ILC. Recent accomplishments have been documented in multiple places, including the proceedings of the 2006 SciDAC meeting, as well as recent invited talks at FNAL and the just held International Computational Accelerator Physics Workshop. VORPAL visualizations have appeared on the cover of Nature and of the proceedings of SciDAC 2006. The advantages of the algorithms implemented within the VORPAL framework are their speed, scalability, and minimal memory usage. The speed comes from the fact that all updates can be written as local operations on grid variables, involving only the nearest neighbors. (There are no global linear equations to solve.) The scalability then derives from this, as such updates require the transfer of only the data on the surfaces of the domains assigned to each processor. To take full advantage of this, VORPAL has within it a set-theory based approach to setting up communications that allows an arbitrary covering decomposition. The result has been demonstrated scalability up the the largest supercomputers available at the time of the last tests, namely to 4000 processors on Seaborg, the NERSC POWER III supercomputer. Finally, as to memory usage, the algorithms and structures within VORPAL ensure that almost no more data than exists with the fields and particles is needed. Thus, it is possible to run a problem with 1.5B degrees of freedom with no more than 24 GB of memory [a]. The FD methods have made important strides in the last decade through the development of embedded boundaries (aka cut cells or conformal boundaries). Important early work was that by Dey and Mittra [2] and this has been refined in the work of Zagorodnov et al [3]. In these papers it was shown that one could obtain high accuracy in the presence of curved boundaries. VORPAL has (to the best of my knowledge) the only parallel implementation of conformal boundaries in a finite difference computational EM application. As noted in our presentation at SciDAC 2006, this has allowed the use of Richardson extrapolation to increase all computations by one higher order. Thus, the implemented second-order algorithm produces results with third-order error. This allows one to obtain accuracy to on part on 10^5 with only about 50 cells per characteristic dimension. The above results rely on the ability to generate meshes, and here is another place where embedded boundary methods have a real advantage. With embedded boundaries, one need not compute the mesh throughout a volume, only at the surface, where one essentially computes only the intersections of the boundary with the mesh and from that computes fractional lengths, areas, and volumes of cells. Consequently, mesh generation parallelizes trivially, and mesh generation is very fast - typically minutes at most on the largest problems - sufficiently fast that for convenience, we regenerate the mesh at each run because the computation is so minor. We currently generate meshes from a python-coded logical function that returns whether a point is inside the cavity. This implies that cavities can be defined through a scripting process. (We have an STL-CAD implementation mostly implemented but not fully tested.) The above two capabilities imply the ability to do error and parameter studies rapidly. For example, to add a deformity to a cavity, one modifies the boundary function through addition of an error term and reruns the simulation. There is no need to go through the cycle of CAD-description-to-mesh-generation-to- code-importation to do a calculation. Streamlining this cycle becomes important for the problem in which one would like to infer the imperfections from the measured spectrum. There has been considerable work in algorithms for FD electromagnetics, including the absolutely stable methods for time integration. These include the work of deRaedt [4], Zheng et al [5], with the latter recently followed up by Fornberg [6]. The first of these is fully explicit (no linear solve), while the latter are methods that require at each stage of the algorithm only to solve a set of tridiagonal systems. Such solves converge in a single iteration with only 6 times the number of numerical operations as an explicit update. Our own work [7] has provided a modification of the Zheng et al and Fornberg methods that is charge conserving, so that Poisson's equation is satisfied. Thus, we can now have absolute stability with implicit methods that require minimal work. This will be important in SciDAC-2 as we model systems in which the needed transverse resolution, dictated by the beam size, is much greater than the longitudinal. Yet another recent advance has been in the development of perfect dispersion algorithms [8], in which the dispersion of perturbations aligned with the beam perfectly follows the vacuum result of omega = kc. This is important for the modeling of relativistic beams in cavities, as the emission of radiation, hence the wake fields, depends sensitively on phase velocity of light relative to the velocity of the beam. Most numerical methods produce short wavelength subluminal waves, which are then artificially radiated by a highly relativistic beam. This "numerical Cerenkov" radiation results in unphysical radiation generated by the beam and ultimately traveling down the pipe or out the HOM couplers. Superluminal waves can be problematic as well, as the interaction between beam and the mode changes, though not as dramatically. The perfect dispersion algorithms eliminate these unphysical effects completely. Finally, we have now shown [9] how to modify our more rapid new algorithm [7] to obtain perfect dispersion and charge conservation simultaneously. We believe that this algorithm will be crucial for end-to-end, self-consistent modeling of the ILC. Higher-order algorithms are available as well. A recent, promising approach to combining those with conformal boundaries is presented in the compact stencil work of [10]. While VORPAL has so far been used in only the time domain, implementing a frequency-domain model is straight forward. VORPAL already has implementations for the Bowers [11] implicit advance through use of matrix methods that call out to the Trilinos parallel linear algebra library. While the code is not in place for conformal boundaries (it is present for planar boundaries), this could be done rapidly in SciDAC-2, were it declared a priority, and this would provide another check on the frequency-domain computations currently being carried out by the SLAC electromagnetics group. Additionally, the VORPAL framework was built very generally, to be able to incorporate any algorithms that can exist on a hexahedral mesh. Thus, finite-element algorithms can be implemented within the VORPAL framework as well, should the case be made. Finally, VORPAL is presently installed at many of the national laboratories, including FNAL, LBNL, JLAB, BNL, and ANL, and at several universities, including the Universities of Texas and California. Scientists at these labs have full access to VORPAL to assist them with their research. [1] C. Nieter and J. R. Cary J. Comp. Phys. 196, 538 (2004). [2] S. Dey and R. Mittra, IEEE Microwave and Guided Wave Lett. v. 7, 273 (1997). [3] I. A. Zagorodnovn, R. Schuhmann and T. Weiland, Int. J. Numer. Model: Elec net, Devices, Fields v. 16, 127 (2003). [4] J. S. Kole, M. T. Figge, and H. De Raedt, Phys. Rev. E v. 64, 066705 (2001). [5] F. Zheng, Z. Chen, and J. Zhang, IEEE Trans. Microwave Theory Techniques v. 48, 1550 (2000). [6] J. Lee and B. Fornberg, J. Comp. App. Math. v. 66, 497 (2003). [7] D. Smithe, J. R. Cary, J. A. Carlsson, in draft. [8] I. Zagorodnov and T. Weiland, Phys. Rev. ST/AB v. 8, 042001 (2005). [9] D. Smithe, J. R. Cary, J. A. Carlsson, in draft. [10] A. Yefet, E. Turkel, App. Num. Math. v. 33, 125 (2000). [11] K. Bowers, Ph.D. thesis, U. Calif. (2001).