Hello, A yearly allocation for the LCRC cluster has been requested with the following updated information: Submitter/PI: Barry Smith Project Name: DVI_Materials Division: MCS Project title: DVI Solvers for Material Science Associated funding: DOE ASCR ARPA-E, FASTMath SciDAC Other Systems: Science: This project uses differential variational inequalities (DVIs) for heterogeneous materials problems, which describe the mesoscale behavior of irradiate damaged materials, for example in a nuclear reactor. The phase field approach is used for modeling microstructure in the mesoscale. Since the diffuse boundary between phases must be localized, one needs to use double obstacle potentials for generating the free energy functional. This results in a differential variational inequality. Our aim is to develop algorithms and software for large-scale DVIs in collaboration with material scientists. Project description: IWe employ coupled Cahn-Hilliard and Allen-Cahn systems with a double obstacle free energy potential to simulate the physics. The model is discretized in time with mixed implicit-explicit integration and in space by finite elements. However, a naive finite element approximation does not guarantee that the discrete solution satifises appropriate constraints. Therefore, we formulate a DVI, which is equivalent to a complementarity problem and provides bounds on the constrained variables This approach in turn allows us to use parallel solvers for complementarity problems in PETSc. We have validated the DVI approach agains the baseline results of the Center for Materials Science of Nuclear Fuel^M(CMSNF). We employed much larger time steps than the conventional finite difference and finite element methods, which is one of the projected benets of the DVI formulation.We have completed preliminary numerical experiments and mathematical analysis for both the Allen-Cahn and Cahn-Hilliard systems that demonstrate mesh-independent convergence rates for this preconditioner. That is, the work required to solve a single timestep grows linearly with the number of unknowns. For now we are making 2 dimensional runs and hope to use at least a 1000 by 1000 grids, with 5 degrees of freedom per grid point and hence at least 5 million unknowns. At each time step one must solve a sequence of linear problems of varying sizes with around 5 million degrees of freedom. We are using the geometric multigrid in PETSc for the linear solves. On a workstation for 100 by 100 grids it takes about 30 seconds per grid point. We plan to use the Intel compilers and MPI, later we may use hybrid programming within a node but for initial work it is all MPI. Project members: Barry Smith, Lois McInnes, Satish Balay, Mihai Amotesci, Todd Munson, Jungho Lee, Lei Wang. Project URL: Current FY Hours Used: undetermined amount New FY Requested allocation: 50000 Q1: 12500 Q2: 12500 Q3: 12500 Q4: 12500 Justification: Thank You, The LCRC Accounts System