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A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and…
A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…
Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms to estimate system…
We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the…
Curve & Lookup Table (LUT) based methods directly map a pixel to the target output, making them highly efficient tools for real-time photography processing. However, due to extreme memory complexity to learn full RGB space mapping, existing…
The adaptive $s$-step CG algorithm is a solver for sparse, symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we…
We investigate a local incremental stationary scheme for the numerical solution of rate-independent systems. Such systems are characterized by a (possibly) non-convex energy and a dissipation potential, which is positively homogeneous of…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and…
Real-time analysis of bio-heat transfer is very beneficial in improving clinical outcomes of hyperthermia and thermal ablative treatments but challenging to achieve due to large computational costs. This paper presents a fast numerical…
We construct a higher-order adaptive method for strong approximations of exit times of It\^o stochastic differential equations (SDE). The method employs a strong It\^o--Taylor scheme for simulating SDE paths, and adaptively decreases the…
Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that,…
A model of a multilayer device with non-trivial geometrical structure and nonlinear dependencies of thermodynamic material properties at cryogenic temperatures is suggested. A considered device, called cryogenic cell, is intended for use in…
The paper considers a time-adaptive method for determination of drug efficacy in a parameter identification problem (PIP) for system of ordinary differential equations (ODE) which describe dynamics of the primary HIV infection. Optimization…
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be solved efficiently and accurately. Traditionally, these…
We introduce the time-dependent restricted active space Configuration Interaction method to solve the time-dependent Schr\"odinger equation for many-electron atoms, and particularly apply it to the treatment of photoionization processes in…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
We have developed a three-dimensional radiative transfer method designed specifically for use with parallel adaptive mesh refinement hydrodynamics codes. This new algorithm, which we call hybrid characteristics, introduces a novel form of…
Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…