A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

A holistic understanding of web design elements

Web design elements are significantly important for web designers to understand target users in terms of effective communication design and to develop a successful web site. However, web design elements generally known are broad and various that are hardly conceived and classified, so many practitioners and design researchers approach to web design elements based on graphic and visual design that mainly focus on print media design. This paper discusses about web design elements in terms of online user experience, as web media certainly differs from print media. It aims to propose a fundamentally new concept, called 'UEDUs: User Experience Design Units' which enables web designers to define web design elements and conceptualise user experience depending on the purpose of web site development.

A conceptual framework for a systematic mapping of layout design principles by using Yin and Yang theory

There are various principles for layout design such as balance, rhythm, unity and harmony, but each principle has often been introduced as a separate concept rather than within an integrated and systematic structure, so that designers and design students have to keep practices for the acquisition of skills. The paper seeks to develop a conceptual framework for a systematic mapping of layout design principles by using Yin and Yang and the Five Elements. Yin and Yang theory explains all natural phenomena with its own conceptual model and facilitates finding harmony and balance between the visual elements in terms of systematic and organic relations. Most common and well-known layout design principles are defined with 10 different resources such as design books and articles, and have been remapped following with the structure of Yin and Yang and the Five Elements. A systematic framework explaining the relationships of design principles was created and 32 design students participated in its efficiency test. The outcome suggests there is a high possibility that the framework can be used in professional fields and design education.

The Quality of Interface Design for Educational Courseware Development in Malaysian Educational Context

Interactive educational courseware has been adopted in diverse education sectors such as primary, secondary, tertiary education, vocational and professional training. In Malaysian educational context, the ministry of education has implemented Smart School Project that aims to increase high level of academic achievement in primary and secondary schools by using interactive educational courseware. However, many researchers have reported that many coursewares fail to accommodate the learner and teacher needs. In particular, the interface design is not appropriately designed in terms of quality of learning. This paper reviews educational courseware development process in terms of defining quality of interface design and suggests a conceptual model of interface design through the integration of design components and interactive learning experience into the development process. As a result, it defines the concept of interactive learning experience in a more practical approach in order to implement each stage of the development process in a seamless and integrated way.

The understanding of avatar design : various types and styles of avatars and the design considerations

People have adopted various formats of media such as graphics, photo and text (nickname) in order to represent themselves when communicate with others online. Avatar is known as a visual form representing a user oneself and one's identity wished. Its form can vary from a two-dimensional model to a three-dimensional model, and can be visualised with various visual forms and styles. In general, two-dimensional images including an animated image are used in online forum communities and live chat software; while three-dimensional models are often used in computer games. Avatar design is often regarded as a graphic designer's visual image creation or a user's output based on one's personal preference, yet it often causes the avatar design having no consideration of its practical visual design and users' interactive communication experience aspects. This paper will review various types and styles of avatar and discuss about avatar design from visual design and online user experience perspectives. It aims to raise a design discourse in avatar design and build up a well-articulated set of design principles for effective avatar design.

Reflective learning through social network sites in design education

Reflective learning is vital for successful practice-led education such as animation, multimedia design and graphic design, and social network sites can accommodate various learning styles for effective reflective learning. In this paper, the researcher studies reflective learning through social network sites with two animation units. These units aim to provide students with an understanding of the tasks and workflows involved in the production of style sheets, character sheets and motion graphics for use in 3D productions for film and television and game design. In particular, an assessment in these units requires students to complete their online reflective journals throughout the semester. The reflective learning has been integrated within the unit design and students are encouraged to reflect weekly learning processes and outcomes. A survey evaluating for students’ learning experience was conducted, and its outcomes indicate that social network site based reflective learning will not be effective without considering students’ learning circumstances and designing peer-to-peer interactions.

Blog and design education : facilitating reflective learning

This paper discusses about effectiveness of blogs for reflective learning in design education. Students in two animation units were asked to complete their online journal via blog in terms of reflective learning. Students were encouraged to respond their weekly outcomes and project development process to their blog and share it with other students. A survey was undertaken to evaluate their learning experience and one of the key outcomes indicates that interaction design for social network is significantly important to blog based learning design.

Metal oxide nanofibres membranes assembled by spin-coating method

Ceramic membranes are of particular interest in many industrial processes due to their ability to function under extreme conditions while maintaining their chemical and thermal stability. Major structural deficiencies under conventional fabrication approach are pin-holes and cracks, and the dramatic losses of flux when pore sizes are reduced to enhance selectivity. We overcome these structural deficiencies by constructing hierarchically structured separation layer on a porous substrate using larger titanate nanofibres and smaller boehmite nanofibres. This yields a radical change in membrane texture. The differences in the porous supports have no substantial influences on the texture of resulting membranes. The membranes with top layer of nanofibres coated on different porous supports by spin-coating method have similar size of the filtration pores, which is in a range of 10–100 nm. These membranes are able to effectively filter out species larger than 60 nm at flow rates orders of magnitude greater than conventional membranes. The retention can attain more than 95%, while maintaining a high flux rate about 900 L m-2 h. The calcination after spin-coating creates solid linkages between the fibres and between fibres and substrate, in addition to convert boehmite into -alumina nanofibres. This reveals a new direction in membrane fabrication.

The effective and the evocative : reflecting on practice-led research approaches in art and design

Early in the practice-led research debate, Steven Scrivener (2000, 2002) identified some general differences in the approach of artists and designers undertaking postgraduate research. His distinctions centered on the role of the artefact in problem-based research (associated with design) and creative-production research (associated with artistic practice). Nonetheless, in broader discussions on practice-led research, 'art and design' often continues to be conflated within a single term. In particular, marked differences between art and design methodologies, theoretical framing, research goals and research claims have been underestimated. This paper revisits Scrivener's work and establishes further distinctions between art and design research. It is informed by our own experiences of postgraduate supervision and research methods training, and an empirical study of over sixty postgraduate, practice-led projects completed at the Creative Industries Faculty of QUT between 2002 and 2008. Our reflections have led us to propose that artists and designers work with differing research goals (the evocative and the effective, respectively), which are played out in the questions asked, the creative process, the role of the artefact and the way new knowledge is evidenced. Of course, research projects will have their own idiosyncrasies but, we argue, marking out the poles at each end of the spectrum of art and design provides useful insights for postgraduate candidates, supervisors and methodologists alike.

Empirical evaluation of a service analysis and design methodology

Service-orientation has gained widespread acceptance and is increasingly being employed as a paradigm for structuring both business and IT architectures. An earlier study of extant service analysis and design methodologies discovered a need for holistic approaches that equally account for both business and software services, which motivated the design of a new, consolidated service analysis and design methodology. A challenge in design-oriented research is to evaluate the utility of the newly created artefacts (here: the methodology), as they are often intended to become part of complex socio-technical systems. Therefore, after presenting a brief overview of the consolidated methodology, the paper discusses possible approaches for the “evaluate” phase of this design-science research process and presents the results of an empirical evaluation conducted in an Action Research study at one of Australia’s largest financial services providers.

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.