Boundary integral methods for singularly perturbed boundary value problems

In this paper we consider boundary integral methods applied to boundary value problems for the positive definite Helmholtz-type problem -DeltaU + alpha U-2 = 0 in a bounded or unbounded domain, with the parameter alpha real and possibly large. Applications arise in the implementation of space-time boundary integral methods for the heat equation, where alpha is proportional to 1/root deltat, and deltat is the time step. The corresponding layer potentials arising from this problem depend nonlinearly on the parameter alpha and have kernels which become highly peaked as alpha --> infinity, causing standard discretization schemes to fail. We propose a new collocation method with a robust convergence rate as alpha --> infinity. Numerical experiments on a model problem verify the theoretical results.

Mouse movements of motion-impaired users: a submovement analysis

Understanding human movement is key to improving input devices and interaction techniques. This paper presents a study of mouse movements of motion-impaired users, with an aim to gaining a better understanding of impaired movement. The cursor trajectories of six motion-impaired users and three able-bodied users are studied according to their submovement structure. Several aspects of the movement are studied, including the frequency and duration of pauses between submovements, verification times, the number of submovements, the peak speed of submovements and the accuracy of submovements in two-dimensions. Results include findings that some motion-impaired users pause more often and for longer than able-bodied users, require up to five times more submovements to complete the same task, and exhibit a correlation between error and peak submovement speed that does not exist for able-bodied users.

Gravity well visibility in haptic interfaces for motion-impaired

Haptic computer interfaces provide users with feedback through the sense of touch, thereby allowing users to feel a graphical user interface. Force feedback gravity wells, i.e. attractive basins that can pull the cursor toward a target, are one type of haptic effect that have been shown to provide improvements in "point and click" tasks. For motion-impaired users, gravity wells could improve times by as much as 50%. It has been reported that the presentation of information to multiple sensory modalities, e.g. haptics and vision, can provide performance benefits. However, previous studies investigating the use of force feedback gravity wells have generally not provided visual representations of the haptic effect. Where force fields extend beyond clickable targets, the addition of visual cues may affect performance. This paper investigates how the performance of motion-impaired computer users is affected by having visual representations of force feedback gravity wells presented on-screen. Results indicate that the visual representation does not affect times and errors in a "point and click" task involving multiple targets.

The effect of multiple haptic distractors on the performance of motion-impaired users

The effect of multiple haptic distractors on target selection performance was examined in terms of times to select the target and the associated cursor movement patterns. Two experiments examined: a) The effect of multiple haptic distractors around a single target and b) the effect of inter-item spacing in a linear selection task. It was found that certain target-distractor arrangements hindered performance and that this could be associated with specific, explanatory cursor patterns. In particular, it was found that the presence of distractors along the task axis in front of the target was detrimental to performance, and that there was evidence to suggest that this could sometimes be associated with consequent cursor oscillation between distractors adjacent to a desired target. A further experiment examined the effect of target-distractor spacing in two orientations on a user’s ability to select a target when caught in the gravity well of a distractor. Times for movements in the vertical direction were found to be faster than those in the horizontal direction. In addition, although times for the vertical direction appeared equivalent across five target-distractor distances, times for the horizontal direction exhibited peaks at certain distances. The implications of these results for the design and implementation of haptically enhanced interfaces using the force feedback mouse are discussed.

Multiple haptic targets for motion-impaired computer users

Although a number of studies have reported that force feedback gravity wells can improve performance in "point-and-click" tasks, there have been few studies addressing issues surrounding the use of gravity wells for multiple on-screen targets. This paper investigates the performance of users, both with and without motion-impairments, in a "point-and-click" task when an undesired haptic distractor is present. The importance of distractor location is studied explicitly. Results showed that gravity wells can still improve times and error rates, even on occasions when the cursor is pulled into a distractor. The greatest improvement is seen for the most impaired users. In addition to traditional measures such as time and errors, performance is studied in terms of measures of cursor movement along a path. Two cursor measures, angular distribution and temporal components, are proposed and their ability to explain performance differences is explored.

The use of cursor measures for motion-impaired computer users

“Point and click” interactions remain one of the key features of graphical user interfaces (GUIs). People with motion-impairments, however, can often have difficulty with accurate control of standard pointing devices. This paper discusses work that aims to reveal the nature of these difficulties through analyses that consider the cursor’s path of movement. A range of cursor measures was applied, and a number of them were found to be significant in capturing the differences between able-bodied users and motion-impaired users, as well as the differences between a haptic force feedback condition and a control condition. The cursor measures found in the literature, however, do not make up a comprehensive list, but provide a starting point for analysing cursor movements more completely. Six new cursor characteristics for motion-impaired users are introduced to capture aspects of cursor movement different from those already proposed.

Using cursor measures to determine appropriate computer input assistance for motion-impaired users

People with motion-impairments can often have difficulty with accurate control of standard pointing devices for computer input. The nature of the difficulties may vary, so to be most effective, methods of assisting cursor control must be suited to each user's needs. The work presented here involves a study of cursor trajectories as a means of assessing the requirements of motion-impaired computer users. A new cursor characteristic is proposed that attempts to capture difficulties with moving the cursor in a smooth trajectory. A study was conducted to see if haptic tunnels could improve performance in "point and click" tasks. Results indicate that the tunnels reduced times to target for those users identified by the new characteristic as having the most difficulty moving in a smooth trajectory. This suggests that cursor characteristics have potential applications in performing assessments of a user's cursor control capabilities which can then be used to determine appropriate methods of assistance.

Perception and haptics

For people with motion impairments, access to and independent control of a computer can be essential. Symptoms such as tremor and spasm, however, can make the typical keyboard and mouse arrangement for computer interaction difficult or even impossible to use. This paper describes three approaches to improving computer input effectivness for people with motion impairments. The three approaches are: (1) to increase the number of interaction channels, (2) to enhance commonly existing interaction channels, and (3) to make more effective use of all the available information in an existing input channel. Experiments in multimodal input, haptic feedback, user modelling, and cursor control are discussed in the context of the three approaches. A haptically enhanced keyboard emulator with perceptive capability is proposed, combining approaches in a way that improves computer access for motion impaired users.

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

Does training improve understanding of core concepts in cognitive behaviour therapy by people with intellectual disabilities? A randomized experiment

Background. People with intellectual disabilities (ID) experience similar or even higher rates of mental health problems than the general population and there is a need to develop appropriate treatments. Cognitive behaviour therapy (CBT) is effective for a wide range of disorders in the general population. However, there is some evidence that people with ID may lack the cognitive skills needed to take part in CBT. Aims. To test if people with ID can learn skills required for CBT, specifically the ability to distinguish between thoughts, feelings, and behaviours and to link thoughts and feelings (cognitive mediation). Method. A randomized independent groups design was used to examine the effect of training in CBT on two tasks measuring CBT skills. Thirty-four adults with ID were randomly allocated to the experimental condition ðN ¼ 18Þ or to the control condition ðN ¼ 16Þ. CBT skills were assessed blind at baseline and after the intervention. Results. The training led to significant improvements in participants’ ability to link thoughts and feelings, and this skill was generalized to new material. There was no effect of training on participants’ ability to distinguish amongst thoughts, feelings, and behaviours. People with ID can, therefore, learn some skills required for CBT. This implies that preparatory training for CBT might be useful for people with ID. The results might be applicable to other groups who find aspects of CBT difficult.

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

The unsteady flow of a weakly compressible fluid in a thin porous layer III: three-dimensional computations

We describe a novel method for determining the pressure and velocity fields for a weakly compressible fluid flowing in a thin three-dimensional layer composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Our approach uses the method of matched asymptotic expansions to derive expressions for all significant process quantities, the computation of which requires only the solution of linear, elliptic, two-dimensional boundary value and eigenvalue problems. In this article, we provide full implementation details and present numerical results demonstrating the efficiency and accuracy of our scheme.