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In the class of immersed boundary (IB) methods, the choice of the delta function plays a crucial role in transferring information between fluid and solid domains. Most prior work has used isotropic kernels that do not preserve the…

Tile B-splines in $\mathbb{R}^d$ are defined as autoconvolutions of the indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $\mathbb{R}^d$. These functions are not piecewise-polynomial,…

We propose a local type of B-bar formulation, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space…

This work introduces a locally refined version of the Adini finite element for the planar biharmonic equation on rectangular partitions with at most one hanging node per edge. If global continuity of the discrete functions is enforced, for…

Based on the continuous interpretation of deep learning cast as an optimal control problem, this paper investigates the benefits of employing B-spline basis functions to parameterize neural network controls across the layers. Rather than…

This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility…

We develop a local polynomial spline interpolation scheme for arbitrary spline order on bounded intervals. Our method's local formulation, effective boundary considerations and optimal interpolation error rate make it particularly useful…

Optimizing k-space sampling trajectories is a promising yet challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction method and sampling trajectories jointly concerning image…

In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The extended Tchebycheff spaces and their dimensions are allowed to…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…

Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…

In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…

We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and…

Sparse grids based on Lagrange polynomials have become one of the staple methods for approximating functions that are high-dimensional and expensive to evaluate, in the context e.g. of PDE-based parametric design exploration. They are…

This contribution introduces the idea of refinement patterns for the generation of optimal meshes in the context of the Finite Element Method. The main idea is to generate a library of possible patterns on which elements can be refined and…

This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…

The discrete element method (DEM) is a powerful tool for simulating granular soils, but its high computational demand often results in extended simulation times. While the effect of particle size has been extensively studied, the potential…

As deep neural networks become the state-of-the-art approach in the field of computer vision for dense prediction tasks, many methods have been developed for automatic estimation of the target outputs given the visual inputs. Although the…