Center For Process Simulation and Design, University of Illinois
Center For Process Simulation and Design, University of Illinois
Center For Process Simulation and Design, University of Illinois
Research objective: For multi-scaling, develop For 1-D phonons we use continuum and one embedded atomistic
method for coupling atomistic and continuum element, we input a traveling wave and plot the wave in both
simulations of solids that obeys the full set of continuum (LHS) and atomic (RHS) regions. Colors show various
mechanics relations, including kinematic compatibility
times. Solution is well represented in all elements.
as well as balance of momentum and energy, without
ad hoc assumptions. In the SDG Hybrid method, we solve for unknown tractions
at atomistic boundary to maintain continuity. Method
Approach: Using the space-time discontinuous inherently maintains balance laws.
Galerkin (SDG) formalism, we maintain continuity and
balance laws across the atomistic/continuum interface continuum atomistic
via flux-based coupling. The SDG method naturally
includes space and time averaging through weak-
Wave amplitude
coupling on boundaries between elements, and thereby
transfers coarse-grained information from atomistic to
continuum regions. We will employ statistical
mechanics methods to repopulate modes on atomistic
side that are unresolved on continuum side.
Research objective: We seek an effective parallel The Simulation of Solidification Problem Using Level Set Method
implementation of a level set method for tracking
the solidification front in simulations of solidification
processes. A parallel solution strategy is a
practical necessity because the simulation problem
is computationally complex as it requires a highly
refined spatial grid and many time steps to attain
the required accuracy.
Broader impact: Unlike standard mesh generation in space, meshing directly in spacetime presents unique
theoretical challenges that are solved and validated by experiments for linear and nonlinear systems. In
concert with new numerical methods, our meshing algorithms promise much more efficient and accurate
simulations for a wide variety of physical phenomena of interest to materials scientists and manufacturers.
Appeared at 20th Annual ACM Symposium on Computational Geometry (SoCG), June 2004.