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Bakgrund: Finjusteringar av hörapparatens förstärkning görs för att validera förstärkningen. Patientens förmåga att kategorisera ljudbilden ligger till grund för de justeringar som görs. Syfte: Att utvärdera en praktiknära metod för finjustering av hörapparater. Metod: Deltagarna (N = 18) fick lyssna på och bedöma ljudbilden för ett talmaterial med slumpade nivåmodifieringar i oktavbandet 4 kHz. Försöksledaren korrigerade ljudbilden utifrån deltagarnas nivåbedömning, till dess att deltagarna upplevde att ljudbilden var naturlig. Deltagarna fick efter halva undersökningen, som intervention, lyssna på en genomgång som förklarade och jämförde de olika ljudbilderna. Resultat: Deltagarnas nivåbedömningar ledde till korrigeringar i oktavbandet som var statistiskt signifikanta, men en normalisering av oktavbandet uppnåddes inte. Efter genomgången kunde fler nivåmodifikationer korrigeras med en statistiskt signifikant skillnad. Nivåmodifikationer som kan kategoriseras som metalliska/skarpa ledde oftare till en statistiskt signifikant korrigering, än nivåmodifikationer som kan kategoriseras som otydliga/dova. Slutsatser: Om finjusteringar av hörapparaterna görs, bör audionomen ha klart för sig att det kan behövas större nivåförändringar i större frekvensband, för att patienten ska ha möjlighet att uppleva en skillnad i ljudbilden i en klinisk miljö., Background: Fine-tuning of the hearing aid amplification is done to validate the amplification. The patient's ability to describe the sound quality lays as a foundation for the fine-tuning. Aim: To evaluate a practice-oriented method for fine-tuning hearing aids. Methods: The participants (N = 18) listened to and evaluated the sound quality for a speech-material with randomized level modifications in the octave band 4 kHz. The sound quality was adjusted according to the participants' evaluation, until a normalized sound quality was perceived by the participants. Halfway through the examination the participants, as an intervention, listened to a briefing which explained and compared differences in the different sound qualities. Results: The participants level evaluation led to adjustment in the octave band that was statistically significant, but a normalization of the octave band could not be achieved. After the briefing a larger number of level modifications were adjusted with a statistical significance. Level modifications which were categorized as metallic/sharp more often led to a statistically significant adjustment compared to level modifications categorized as unclear/dull. Conclusions: If fine-tuning of hearing aids is done, the audiologist should be aware that bigger level adjustment in broad bands might be needed, for the patient to be able to notice a difference in sound quality in a clinical setting.

A technique for coupling an intrusive and non-intrusive uncertainty quantification method is proposed. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. A strongly stable coupling procedure between the two methods at an interface is constructed. The efficiency of the hybrid method is exemplified using a hyperbolic system of equations, and verified by numerical experiments.

We consider a stochastic analysis of the non-linear viscous Burgers’ equation and focus on the comparison between intrusive and non-intrusive uncer- tainty quantification methods. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. The two methods are applied to a provably stable formulation of the viscous Burgers’ equation, and compared. As measures of comparison: variance size, computational efficiency and accuracy are used.

The two dimensional advection-diffusion equation in a stochastically varying geometry is considered. The varying domain is transformed into afixed one and the numerical solution is computed using a high-order finite difference formulation on summation-by-parts form with weakly imposed boundary conditions. Statistics of the solution are computed non-intrusively using quadrature rules given by the probability density function of the random variable. As a quality control, we prove that the continuous problem is strongly well-posed, that the semi-discrete problem is strongly stable and verify the accuracy of the scheme. The technique is applied to a heat transfer problem in incompressible flow. Statistical properties such as confidence intervals and variance of the solution in terms of two functionals are computed and discussed. We show that there is a decreasing sensitivity to geometric uncertainty as we gradually lower the frequency and amplitude of the randomness.

We study an incompletely parabolic system in three space dimensions with stochastic boundary and initial data. We show how the variance of the solution can be manipulated by the boundary conditions, while keeping the mean value of the solution unaffected. Estimates of the variance of the solution is presented both analytically and numerically. We exemplify the technique by applying it to an incompletely parabolic model problem, as well as the one-dimensional compressible Navier-Stokes equations.

We consider a hyperbolic system in one space dimension with uncertainty in the boundary and initial data. Our aim is to show that di erent boundary conditions gives different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution is presented. As an application, we study the effect of this technique on a subsonic outow boundary for the Euler equations.

Our focus in this paper is on the fundamental system of partial differential equation with boundary conditions (the continuous problem) that all types of numerical methods must respect. First, a constant coefficient hyperbolic system of equations which turns into a variable coefficient system of equations by transforming to a non-cartesian domain is considered. We discuss possible formulations of time-dependent boundary conditions leading to well-posed or strongly well-posed problems. Next, we re-use the previous theoretical derivations for the problem with boundary conditions applied at the wrong position and/or with an incorrect normal (a typical result with a less than perfect mesh generator). Possible error sources are discussed and a crude error estimate is derived.