Designing with an underdeveloped computational composite for materials experience

In response to the urge for multidisciplinary development of computational composites, designers and material scientists are increasingly involved in collaborative projects to valorize these technology-push materials in the early stages of their development. To further develop the computational composites, material scientists need designer’s...

On the use of rigid body modes in the deflated preconditioned conjugate gradient method

Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper...

Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials

Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms....

The Deflated Preconditioned Conjugate Gradient Method Applied to Composite Materials

Simulations with composite materials often involve large jumps in the coefficients of the underlying stiffness matrix. These jumps can introduce unfavorable eigenvalues in the spectrum of the stiffness matrix. We show that the rigid body modes; the translations and rotations, of the disjunct rigid bodies in the composite material correspond to...

Comparison of the deflated preconditioned conjugate gradient method and parallel direct solver for composite materials

The demand for large FE meshes increases as parallel computing becomes the standard in FE simulations. Direct and iterative solution methods are used to solve the resulting linear systems. Many applications concern composite materials, which are characterized by large discontinuities in the material properties. An example of such a material is...

On the use of rigid body modes in the deflated preconditioned conjugate gradient method

Large discontinuities in material properties, such as encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the Preconditioned Conjugate Gradient (PCG) method. This paper...

Preconditioned conjugate gradient method enhanced by deflation of rigid body modes applied to composite materials.

Development of a solver for large algebraic system from structural mechanics

Improving multigrid for 3-D electro-magnetic diffusion on stretched grids

We evaluated multigrid techniques for 3D diffusive electromagnetism. The Maxwell equations and Ohm's law were discretised on stretched grids, with stretching in all coordinate directions. We compared standard multigrid to alternative multigrid approaches with linewise smoothing and semi-coarsening, both as a stand-alone solver and as a...