Efficient Newton‐multigrid FEM solver for multifield nonlinear coupled problems applied to thixoviscoplastic flows

نویسندگان

چکیده

Abstract This note is concerned with efficient Newton‐multigrid finite element method (FEM) solver for multifield nonlinear flow problems. In our approach, FEM solver, we advantageously use the delicate symbiosis aspects of problem settings approximations, and algorithmic tools to obtain numerical solutions. We concretize ideas on thixoviscoplastic It a two‐field coupled problem. And beside integrated nonlinearity within momentum microstructure equations, problems induce two‐way coupling. As far as solutions are concerned, set in suitable variational form corresponding wellposedness analysis develop techniques solver. Indeed, study not an intellectual exercise, rather it foundation approximate well development base investigations error results published Proc. Appl. Math. Mech . continue series, proceed monolithic The based Newton's geometric multigrid treat coupling So, Local Pressure Schur Complement (LPSC) concept solve mesh's elements, outer blocks Gauss‐Seidel iteration update global Furthermore, handle combined adaptive discrete methods. adaptivity step‐length control differencing Jacobian calculations, while convergence linear made match requirement accordingly. solver's parameters solely dependent actual rate provide performance lid‐driven cavity flow.

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ژورنال

عنوان ژورنال: Proceedings in applied mathematics & mechanics

سال: 2023

ISSN: ['1617-7061']

DOI: https://doi.org/10.1002/pamm.202300062