Related papers: A shape derivative approach to domain simplificati…

Parametric shape optimization aims at minimizing an objective function f(x) where x are CAD parameters. This task is difficult when f is the output of an expensive-to-evaluate numerical simulator and the number of CAD parameters is large.…

Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…

In a recent paper [{\em F. Bernal, J. Mor\'on-Vidal and J.A. Acebr\'on, Comp.$\&$ Math. App. 146:294-308 (2023)}] an hybrid supercomputing algorithm for elliptic equations has been put forward. The idea is that the interfacial nodal…

This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…

Partial differential equations (PDEs) with multiple scales or those defined over sufficiently large domains arise in various areas of science and engineering and often present problems when approximating the solutions numerically. Machine…

We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain…

Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…

The cost of large scale data collection and annotation often makes the application of machine learning algorithms to new tasks or datasets prohibitively expensive. One approach circumventing this cost is training models on synthetic data…

In this paper we present a methodology that allows the efficient computation of the topological derivative for semilinear elliptic problems within the averaged adjoint Lagrangian framework. The generality of our approach should also allow…

This paper explores an efficient Lagrangian approach for evolving point cloud data on smooth manifolds. In this preliminary study, we focus on analyzing plane curves, and our ultimate goal is to provide an alternative to the conventional…

For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…

This manuscript presents an adaptive high order discretization technique for elliptic boundary value problems. The technique is applied to an updated version of the Hierarchical Poincar\'e-Steklov (HPS) method. Roughly speaking, the HPS…

Domain generalization typically requires data from multiple source domains for model learning. However, such strong assumption may not always hold in practice, especially in medical field where the data sharing is highly concerned and…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…

Binary image based classification and retrieval of documents of an intellectual nature is a very challenging problem. Variations in the binary image generation mechanisms which are subject to the document artisan designer including drawing…

As a popular geometric representation, point clouds have attracted much attention in 3D vision, leading to many applications in autonomous driving and robotics. One important yet unsolved issue for learning on point cloud is that point…

Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…

Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…