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A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition…
Many multiscale problems have a high contrast, which is expressed as a very large ratio between the media properties. The contrast is known to introduce many challenges in the design of multiscale methods and domain decomposition…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
We extend the divergence preserving cut finite element method presented in [T. Frachon, P. Hansbo, E. Nilsson, S. Zahedi, SIAM J. Sci. Comput., 46 (2024)] for the Darcy interface problem to unfitted outer boundaries. We impose essential…
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as…
Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such…
A balancing domain decomposition by constraints (BDDC) algorithm with adaptive primal constraints in variational form is introduced and analyzed for high-order mortar discretization of two-dimensional elliptic problems with high varying and…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer.…
We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with a mixed three-field formulation with weak stress symmetry. The fluid flow is modeled with a…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…