Force-Based Atomistic/Continuum Blending for Multilattices
Provides a rigorous theoretical foundation for atomistic/continuum blending in multilattices, addressing a key bottleneck in multiscale modeling of materials with defects.
The paper formulates the BQCF method for multilattices and provides rigorous error estimates, achieving a convergent multiscale method for point defects with a proven convergence rate in computational cost, demonstrated on a graphene defect.
We formulate the blended force-based quasicontinuum (BQCF) method for multilattices and develop rigorous error estimates in terms of the approximation parameters: atomistic region, blending region and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone--Wales defect in graphene.