Outputs (23)

A Shape-Newton method for free-boundary problems subject to the Bernoulli boundary condition (2024)
Journal Article
Fan, Y., Billingham, J., & van der Zee, K. (2024). A Shape-Newton method for free-boundary problems subject to the Bernoulli boundary condition. SIAM Journal on Scientific Computing, 46(6), A3599-A3627. https://doi.org/10.1137/23M1590263

We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the nonlinear Bernoulli equation. The method is a Newton-like scheme that employs shape derivatives of the governing... Read More about A Shape-Newton method for free-boundary problems subject to the Bernoulli boundary condition.

Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids (2024)
Journal Article
ten Eikelder, M. F., van der Zee, K. G., & Schillinger, D. (2024). Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids. Journal of Fluid Mechanics, 990, Article A8. https://doi.org/10.1017/jfm.2024.502

The prototypical diffuse-interface model for incompressible fluid mixtures is the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model. Despite its foundation in continuum mixture theory, it is not fully compatible with this theory due to the diffusive flu... Read More about Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids.

Controlling ZIF-67 film properties in water-based cathodic electrochemical deposition (2024)
Journal Article
Elsayed, E., Brevis, I., Pandiyan, S., Wildman, R., van der Zee, K. G., & Tokay, B. (2024). Controlling ZIF-67 film properties in water-based cathodic electrochemical deposition. Journal of Solid State Chemistry, 338, Article 124820. https://doi.org/10.1016/j.jssc.2024.124820

One of the main approaches to increase the surface area of a substrate is through depositing a film of a porous materials such as Zeolite imidazole framework (ZIF). ZIF films have shown surpassing capabilities because of their zeolite-like features,... Read More about Controlling ZIF-67 film properties in water-based cathodic electrochemical deposition.

Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach (2024)
Journal Article
Brevis, I., Muga, I., Pardo, D., Rodriguez, O., & van der Zee, K. G. (2024). Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach. Computers and Mathematics with Applications, 164, 139-149. https://doi.org/10.1016/j.camwa.2024.04.006

The efficient approximation of parametric PDEs is of tremendous importance in science and engineering. In this paper, we show how one can train Galerkin discretizations to efficiently learn quantities of interest of solutions to a parametric PDE. The... Read More about Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach.

A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities (2023)
Journal Article
ten Eikelder, M. F. P., Van Der Zee, K. G., Akkerman, I., & Schillinger, D. (2023). A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities. Mathematical Models and Methods in Applied Sciences, 33(01), 175-221. https://doi.org/10.1142/S0218202523500069

Over the last decades, many diffuse-interface Navier-Stokes Cahn-Hilliard (NSCH) models with non-matching densities have appeared in the literature. These models claim to describe the same physical phenomena, yet they are distinct from one another. T... Read More about A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities.

Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights (2022)
Journal Article
Brevis, I., Muga, I., & van der Zee, K. G. (2022). Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights. Computer Methods in Applied Mechanics and Engineering, 402, Article 115716. https://doi.org/10.1016/j.cma.2022.115716

There is tremendous potential in using neural networks to optimize numerical methods. In this paper, we introduce and analyse a framework for the neural optimization of discrete weak formulations, suitable for finite element methods. The main idea of... Read More about Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights.

Linearization of the Travel Time Functional in Porous Media Flows (2022)
Journal Article
Rourke, C. J., Houston, P., Rourke, C., & van der Zee, K. G. (2022). Linearization of the Travel Time Functional in Porous Media Flows. SIAM Journal on Scientific Computing, 44(3), B531-B557. https://doi.org/10.1137/21M1451105

The travel time functional measures the time taken for a particle trajectory to travel from a given initial position to the boundary of the domain. Such evaluation is paramount in the postclosure safety assessment of deep geological storage facilitie... Read More about Linearization of the Travel Time Functional in Porous Media Flows.

Projection in negative norms and the regularization of rough linear functionals (2022)
Journal Article
Millar, F., Muga, I., Rojas, S., & Van der Zee, K. G. (2022). Projection in negative norms and the regularization of rough linear functionals. Numerische Mathematik, 150(4), 1087-1121. https://doi.org/10.1007/s00211-022-01278-z

In order to construct regularizations of continuous linear functionals acting on Sobolev spaces such as W01,q(Ω), where 1 < q< ∞ and Ωis a Lipschitz domain, we propose a projection method in negative Sobolev spacesW-1,p(Ω) , pbeing the conjugate expo... Read More about Projection in negative norms and the regularization of rough linear functionals.

Discretization of linear problems in banach spaces: Residual minimization, nonlinear petrov-galerkin, and monotone mixed methods (2020)
Journal Article
Muga, I., & Van Der Zee, K. G. (2020). Discretization of linear problems in banach spaces: Residual minimization, nonlinear petrov-galerkin, and monotone mixed methods. SIAM Journal on Numerical Analysis, 58(6), 3406-3426. https://doi.org/10.1137/20M1324338

This work presents a comprehensive discretization theory for abstract linear operator equations in Banach spaces. The fundamental starting point of the theory is the idea of residual minimization in dual norms and its inexact version using discrete d... Read More about Discretization of linear problems in banach spaces: Residual minimization, nonlinear petrov-galerkin, and monotone mixed methods.

A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma (2020)
Journal Article
Curtin, L., Hawkins-Daarud, A., Porter, A. B., van der Zee, K. G., Owen, M. R., & Swanson, K. R. (2020). A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma. Bulletin of Mathematical Biology, 82(11), Article 143. https://doi.org/10.1007/s11538-020-00814-y

Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have su... Read More about A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma.