Related papers: Fast and accurate method for computing non-smooth …
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…
Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load,…
3D representations of highly deformable 3D models, such as dynamic 3D meshes, have recently become very popular due to their wide applicability in various domains. This trend inevitably leads to a demand for storage and transmission of…
We introduce a model-based iterative method to obtain shear modulus images of tissue using magnetic resonance elastography. The method jointly finds the displacement field that best fits multifrequency tissue displacement data and the…
This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…
This paper deals with time-optimal control of nonlinear continuous-time systems based on direct collocation. The underlying discretization grid is variable in time, as the time intervals are subject to optimization. This technique differs…
It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In the last years, several solution concepts were proposed that…
A trademark of nonlinear, time-dependent, convection-dominated problems is the spontaneous formation of non-smooth macro-scale features, like shock discontinuities and non-differentiable kinks, which pose a challenge for high-resolution…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
We introduce a meshless method for solving both continuous and discrete variational formulations of a volume constrained, nonlocal diffusion problem. We use the discrete solution to approximate the continuous solution. Our method is…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
A new method is developed for solving optimal control problems whose solutions are nonsmooth. The method developed in this paper employs a modified form of the Legendre-Gauss-Radau orthogonal direct collocation method. This modified…
We propose a novel approach to the linear viscoelastic problem of shear-deformable geometrically exact beams. The generalized Maxwell model for one-dimensional solids is here efficiently extended to the case of arbitrarily curved beams…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
We present a novel way of deciding when and where to refine a mesh in probability space in order to facilitate the uncertainty quantification in the presence of discontinuities in random space. A discontinuity in random space makes the…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…