Related papers: An approximate block factorization preconditioner …
In this paper, we design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a structure-preserving finite-element approximation with…
Achieving robust control and optimization in high-fidelity physics simulations is extremely challenging, especially for evolutionary systems whose solutions span vast scales across space, time, and physical variables. In conjunction with…
Mixing is an omnipresent process in a wide-range of industrial applications, which supports scientific efforts to devise techniques for optimising mixing processes under time and energy constraints. In this endeavor, we present a…
Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid the generation of body-fitted meshes and the use of graph…
The shrinking core model describes the reaction of a spherical solid particle with a surrounding fluid. In this work, we revisit the SCM by deriving it from the underlying physical processes and performing a careful non-dimensionalisation,…
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…
In this paper, we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems. One type of the preconditioners are based on the nested (or recursive) Schur complement, the other is…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…
In this paper we study the linear systems arising from discretized poroelasticity problems. We formulate one block preconditioner for the two-filed Biot model and several preconditioners for the classical three-filed Biot model under the…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
Under consideration are multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsmooth convex coupling terms penalizing linear mixtures of the components. We…
The properties of a block preconditioner that has been successfully used in finite element simulations of large scale ice-sheet flow is examined. The type of preconditioner, based on approximating the Schur complement with the mass matrix…
When solving linear systems arising from PDE discretizations, iterative methods (such as Conjugate Gradient, GMRES, or MINRES) are often the only practical choice. To converge in a small number of iterations, however, they have to be…
The simulation of soil-structure interaction problems involving two-phase materials poses significant challenges in geotechnical engineering. These challenges arise due to differences in material stiffnesses, the interaction between…
In this paper, we compute the stationary states of the multicomponent phase-field crystal model by formulating it as a block constrained minimization problem. The original infinite-dimensional non-convex minimization problem is approximated…
In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…
We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and…