Multiscale Methods

Highlights

Contour plots of concentration in a 3D corrosion problem

A hybrid meshfree discretization to improve the numerical performance of peridynamic models

The four symmetry groups (up to a change in orientation) of the elasticity tensor in 2D.

A new proof that the number of linear elastic symmetries in two dimensions is four

Hat shape three-point bending test simulation

An FEM-based peridynamic model for failure analysis of unidirectional fiber-reinforced laminates

Largest connected component of the 2019 peridynamics co-authorship network

The evolution of the peridynamics co-authorship network

Simulations of a two-dimensional Riemann problem with a nuclear EoS using a third-order accurate RKDG method in thornado.

Discontinuous Galerkin Method for Supernova Hydrodynamics with Nuclear Equations of State

Example validations of key physics measurements compared to XGC-only reference simulation

Spatial Core-Edge Coupling of the Particle-in-Cell Gyrokinetic Codes GEM and XGC

Solution profiles of the scalar flux for various methods

Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport

Numerical errrors from simulation of a radiating sphere.

Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods

Distribution of displacement gradients in a three-point bending test. High gradients are concentrated around the applied load point (top center) as well as at the supports (bottom left and right) and at the crack tip (bottom center).

Overall equilibrium in the coupling of peridynamics and classical continuum mechanics

Convergence rates of the NLS method with and without acceleration.

Analysis of a new implicit solver for a semiconductor model

Computation time for the iterative solvers on a proto-neutron star deleptonization problem

A DG-IMEX method for two-moment neutrino transport: Nonlinear solvers for neutrino-matter coupling

Novel anisotropic peridynamic kernels. Left: plane strain peridynamic kernel derived from a 3D cubic material model. Right: 2D peridynamic kernel for a square material model.

Anisotropic two-dimensional, plane strain, and plane stress models in classical linear elasticity and bond-based peridynamics

Bond-based peridynamics: A tale of two Poisson’s ratios

$The solution manifold for different parameters is explored and compressed in the offline learning stage. The constructed reduced model faithfully reproduces the solution manifold with only 10 basis functions. Parameter variability of the model with respect to different fractional exponents (left & middle). The error of the reduced model and error estimates (right).$

A model order reduction method for non-classical models of diffusion

Concentration evolution in a metallic corrosion problem. Top: reference solution. Bottom: solution with the proposed absorbing boundary conditions

Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

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