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The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
It is well established that formulating an effective constraint model of a problem of interest is crucial to the efficiency with which it can subsequently be solved. Following from the observation that it is difficult, if not impossible, to…
The development of materials with specific structural properties is of huge practical interest, for example, for medical applications or for the development of light weight structures in aeronautics. In this article, we combine shape…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…
Particle and ensemble filters are increasingly utilized for inference, optimization, and forecast; however, both filtering methods use discrete distributions to simulate continuous state space, a drawback that can lead to degraded…
An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretization of fracture mechanics problems with well-conditioned extended/generalized finite elements. The deflation space…
Transformer-based models have advanced the field of question answering, but multi-hop reasoning, where answers require combining evidence across multiple passages, remains difficult. This paper presents a comprehensive evaluation of…
In this study, a distinct reconfigurable fault-tolerant flight control strategy is addressed for mitigating one of the persistent safety-critical issue, i.e. loss of control triggered by actuator faults. The attainable acceleration set…
We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
The increasing penetration of renewable generation introduces uncertainty into power systems, challenging traditional deterministic optimization methods. Chance-constrained optimization offers an approach to balancing cost and risk;…
This paper reported a general noninterferometric high-accuracy quantitative phase imaging (QPI) method for arbitrary complex valued objects. Given by a typical 4f optical configuration as the imaging system, three frames of small-window…
Wirelessly connected devices can collaborately train a machine learning model using federated learning, where the aggregation of model updates occurs using over-the-air computation. Carrier frequency offset caused by imprecise clocks in…
We present an algorithmic contribution to improve the efficiency of robust trim-fitting in outlier affected geometric regression problems. The method heavily relies on the quick sort algorithm, and we present two important insights. First,…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…
This work illustrates the possibility to apply the Fast Fourier Transformation to obtain the integrals of the Boundary Element Method (BEM) on arbitrary shapes. The procedure is inspired by the technique used with great success within the…
A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…
Algorithms for partition refinement are actively studied for a variety of systems, often with the optimisation called Hopcroft's trick. However, the low-level description of those algorithms in the literature often obscures the essence of…
We rewrite the standard nodal virtual element method as a generalised gradient method. This re-formulation allows for computing a reliable and efficient error estimator by locally reconstructing broken fluxes and potentials on elemental…