Survey on Instruction Selection: An Extensive and Modern Literature Review

Instruction selection is one of three optimisation problems involved in the code generator backend of a compiler. The instruction selector is responsible of transforming an input program from its target-independent representation into a target-specific form by making best use of the available machine instructions. Hence instruction selection is a crucial part of efficient code generation. Despite on-going research since the late 1960s, the last, comprehensive survey on the field was written more than 30 years ago. As new approaches and techniques have appeared since its publication, this brings forth a need for a new, up-to-date review of the current body of literature. This report addresses that need by performing an extensive review and categorisation of existing research. The report therefore supersedes and extends the previous surveys, and also attempts to identify where future research should be directed.Comment: Major changes: - Merged simulation chapter with macro expansion chapter - Addressed misunderstandings of several approaches - Completely rewrote many parts of the chapters; strengthened the discussion of many approaches - Revised the drawing of all trees and graphs to put the root at the top instead of at the bottom - Added appendix for listing the approaches in a table See doc for more inf

Target Code Selection by Tilling AST with the Use of Tree Pattern Pushdown Automaton

A new and simple method for target code selection by tilling an abstract syntax tree is presented. As it is usual, tree patterns corresponding to target machine instructions are matched in the abstract syntax tree. Matching tree patterns is performed with the use of tree pattern pushdown automaton, which accepts all tree patterns matching the abstract syntax tree in the linear postfix bar notation and represents a full index of the abstract syntax tree for tree patterns. The use of the index allows to match patterns quickly, in time depending on the size of patterns and not depending on the size of the tree. The selection of a particular target instruction corresponds to a modification of the abstract syntax tree and also a corresponding incremental modification of the index is performed. A reference to a fully functional prototype is provided

On Tree Pattern Matching by Pushdown Automata

Tree pattern matching is an important operation in Computer Science on which a number of tasks such as mechanical theorem proving, term-rewriting, symbolic computation and non-procedural programming languages are based on. Work has begun on a systematic approach to the construction of tree pattern matchers by deterministic pushdown automata which read subject trees in prefix notation. The method is analogous to the construction of string pattern matchers: for given patterns, a non-deterministic pushdown automaton is created and then it is determinised. In this first paper, we present the proposed non-deterministic pushdown automaton which will serve as a basis for the determinisation process, and prove its correctness.

Lily: A parser generator for LL(1) languages

This paper discusses the design and implementation of Lily, a language for generating LL(1) language parsers, originally designed by Dr. Thomas J. Sager of the University of Missouri--Rolla. A method for the automatic generation of parser tables is described which creates small, highly optimized tables, suitable for conversion to minimal perfect hash functions. An implementation of Lily is discussed with attention to design goals, implementation of parser table generation, and table optimization techniques. Proposals are made detailing possibilities for further augmentation of the system. Examples of Lily programs are given as well as a manual for the system

Evolution for our time: a theory of legal memetics

The purpose of this paper is to explore the significance for legal thought of recent developments in evolutionary theory which are associated with the notion of 'memetics'. 'Memetics' aims to account for processes of cultural transmission and change using a version of the 'genetic metaphor'. This is the idea that patterns of cultural evolution are closely analogous to those which occur in the natural world as a result of the interaction between genes, organisms and environments. At a further, more ambitious level, the initial metaphor gives way to a search for mechanisms which unite biological and cultural evolution. Identifying these general evolutionary mechanisms is part of a wide-ranging, interdisciplinary research agenda.legal evolution, memes, path dependence, employment contract, corporate governance

Discursive Designing Theory - Towards a Theory of Designing Design -

Discursive Designing Theory - Towards a Theory of Designing Design- Juergen Faust Motivated by the immature theoretical framework of design, this thesis employs transdisciplinary discourse to provide a contemporary and forward-looking model of design and design theory, as well as the linkages between the two, along with the necessary methodology. The discourse involves research into the current understanding of design, its principles, its practice and conceptual framework. The methodology developed and employed in this thesis can be outlined in five steps: 0. Design briefing 1. Developing a conceptual model based on the writings of Michel Foucault and Helmut Krippendorff. 2. Presenting the model in a written form. 3. Using accounts of conferences as tools for Designing Design and building monuments. 4. Interrogating the theory through an expert system. 5. Summarising and evaluating the findings. Design Briefing The present study delves into design, and into the design of theory. In Chapter A.1.6, a summary of Chapter A.0−A.1.5 is given, highlighting the underlying discourse. As shown, the theory behind this work is based on a hypothesis, which cannot be proved experimentally, or deduced from experimental data, at least at the time of its construction. Therefore, it needs to be understood that the case studies (A.3.2−A.3.5) in this thesis are not intended to serve as experiments that were conducted in order to prove the theory; rather, these case studies are design cases—products and artefacts—and should be viewed as discourse frameworks that can be adopted to design design. As described in Chapter 3.1, these are elements of monuments—in reference to Raichman (1988)—that have resulted from the discursive strategies and were designed within a community of designers, allowing the design understanding to be shaped. Methodologically, the theory is created through an indication of differences. These differences were elaborated on in the literature review, and can be explained using either logic-based or hermeneutical metaphors. As the latter approach is more flexible, it might be more applicable to the design environment. The generated knowledge can be located in three areas—design knowledge, epistemology, methodology (the process to get there), and phenomenology (the composition of the artefacts). While the main focus of this thesis has been on theory design, it was also important to delineate how to get there, as well as analyse the questionable differences between theory and practice, since they are ideal types that mark the extreme ends of a continuum (Jonsen and Toulmin 1988, p.36). The work presented in this thesis was conducted in a circular manner, like a design process, in order to encapsulate the instance. Therefore, essential topics reappear, allowing them to be reframed and newly contextualised. Chapter 0.0 to 0.7 reperesent the introductory part of this work. Thus, the content presented could be referred to as ‘the briefing’—as a parallel to a design case—to provide the background. It shows the motivation, a first hypothesis, some methodological considerations, and the research design and decisions. The aim is to provide insight into the phenomenon of interest and discuss some preconceptions. Thus, these introductory chapters provide orientation through locating some statements of the provided (design) discourse. Developing a conceptual model based on the writings of Michel Foucault and Helmut Krippendorff. As a follow up, Section A consists of several key components, and encompasses the research methodology specificity, its theoretical underpinning, and its connection to design, a reframing and contextualisation. This section also provides the means to overcome the discrepancy between researching and designing. Therefore, in Chapter A1−A1.6, a more substantial discourse of design is provided, along with the theory and the essential knowledge. Here, we can see the method in operation, as a patching of discursive statements—akin to an additive process of designing. Clearly, the attempt made here belongs to the constructivist epistemology, as the idea of design is a mental construct. Nonetheless, the aim is to provide a broad perspective of what can be presently observed in the design field. The employed methodology strategically aims to overcome the divide between designing and researching—between acting and reflecting—in order to provide a conceptual model. Still, it also makes the designing practice a conscious process, whereby theory is designed through discourse. Such discourse is revealed within the discovery of textual statements based on an extensive literature review, as well as through the discovery of textual statements from organised interactive conferences. The theory developed here is, in fact, a theory derived from theory, and is shaped through finding patterns and the simplification of the overall structure they form. In A.2, the concept of discourse and its designing quality is revealed. It shows how discourse, as the guiding method, is ‘excavated’ from the writings of Michel Foucault and Helmut Krippendorff. Methodologically, Michel Foucault’s ‘Archeology of Knowledge’ was analysed against and parallel to Helmut Krippendorff’s ‘Semantic Turn’, as these sources are complementary to each other. The goal of this process is a comparison of statements, yielding reasoning towards discourse and design discourse. In sum, this analysis helped reveal that it is a matter of design how the discourse is provided. The outcome of the aforementioned comparison is very interesting and satisfying. The findings revealed a difference in discourse, because engineering and design discourses are informed by rhetoric of design, rhetoric of deliberation, in opposite to humanistic discourse, which consumes textual objects (Perelman 1999). The discursive designing process within these chapters reveals some important elements, such as the conceptual frame of politics, referred to in Foucault’s discourse explorations. According to the author, power is a generating force in shaping discourse (Faucault 1980, p.119). In contrast, Krippendorff (1995b) sees power as emanating from language, which can be overcome through avoiding the construction of certain language. In the research presented, the designing practice that took place during the conferences, as well as the aforementioned notions, play a role, as was shown in Chapter 3. Power, as it was experienced, is unavoidable. Yet, rather than seeing it as a problem, it should be viewed as a generating force. A second more substantial question arises around the notion of discontinuity (A.2.3), which is essential in Foucault’s concept. According to Krippendorff, knowledge is not partitioned; it rather provides continuity through the various disciplines. As this research shows, this view should not be seen as an opposite to Foucault’s concept of discontinuity, because statements can refer to the same object, but coming from a discontinuous field, from various disciplines. In other words, as design discourse can be viewed as a discourse hosted by various disciplines, it is discontinuous! With respect to Foucault’s concern of grasping of statements, the main goal of this thesis is to provide support for this perspective. As the author noted, the grasping of the statements needs to follow the exact specificity of their occurrence (Foucault 1972). The prudence and success of dissociating statements from their original context to place them in a new context is questionable, since no discontinuity can be ignored (Foucault 1972). Often, rather than paraphrasing the text so that it reflects one’s own understanding of it, the result is a mere citation of the original texts and con-texts. The awareness of discontinuity does not allow for this thesis to be presented according to the positivistic paradigm. Thus, rather than stitching the chapters together, as if they would naturally support each other, there might be some discontinuity ‘logic’. Presenting the model in a written form. In Chapter A.2.5 to A.2.7, further perspectives on the various elements of this thesis are revealed, in reference to the discussions presented in the preceding chapters. Scientific discourse, in Krippendorff’s (2006) view, is misleading, since the design activities are different from those involved in science, which focus on search for patterns, and are thus always driven by the past. However, designers are not motivated by the quest for knowledge (patterns), by the challenges, or conflicts that need to be resolved. Rather, they are motivated by opportunities for creating something better (patterns), or by the potential for introducing variations. In sum, designers generate various versions of the future, as they are always interested in the possibilities (variables) and realistic paths (Krippendorff 2006, p.28). Discursive designing of design theory is seen in this way. It is an overcoming of the divide between the past and the process of generating the future, since statements are driven by the past. The monument that emerges as a result, as well as the resulting theory, is thus the future generated by patterning past statements into something new—something we can call future. Generating future in discourse is common for designers, as shown in A.2.6. Designers live in discourse, as sketching is a kind of dialogue (Cross 2007). If not working on design theories, designers produce discourse in conveyance matter, but do not necessary generate knowledge. Drawings and texts serve as evidence of a discourse held, rather than being the discourse itself. Design discourse can be conveyed in various textual forms. Designers turn documents into monuments (Rajchman 1988) when creating objects based on documents. Such dialogues, such discourse, and specifically the design discourse, follow ‘rules’. These ‘rules’ lie in connections with textual matter, with constructed artefacts, with the community of its practitioners, its recurrent practices, and boundaries that justify its identities to outsiders (Krippendorff 2006). In Chapter A2.7, the difference among discourse, discourse analysis and discourse practice is clarified. Discourse practice is not limited by language, as it relies on textual matter. On the other hand, discursive analysis involves search for discourses, discourse formations and rules. It has transformed into the analysis of media texts and talks, the relation between discourse and pictures, photographs or film and many other fields, including therapeutic discourse (van Dijk 1989). While the aforementioned process yields valid results, research that produces explicit knowledge is more desirable. Communication through images is often not accessible for individuals outside the design community (Robbins 1997). Still, practice-based research is what designers do (Dorst 2008a). The differentiation between reflective practice and research should remain (Hart 2006), since the latter is the methodical search for knowledge, while the same is not always true for the former (Friedman 2003). Even though design knowledge arises from practice, not all (design) practice is systematic and methodological. Accounts of conferences as tools for Designing Design and building monuments. Several examples of a systematic design practice and methodology are provided in Chapter 3. While an overview of the setting and method is provided in Chapter 3.1, the conferences included in this study, and the discourse summaries they generated, are presented in Chapter 3.2−3.4. The process of designing these events and evaluating their respective outcomes was very informative for the search for theory. Moreover, the theory itself has led to the discourse of the presented designing design theory. On the other hand, not all conferences were relevant for this study, as not all design practice has been successful in providing knowledge. In three of the conferences held during the period of this study, the design practice was only partially successful. In one instance, the possible knowledge yielded was not sufficiently clear, since it was not documented in usable form. The conference reflection yielded results similar to those arising from the discursive practice that took place when excavating texts. Discourse based on the previously generated textual matter shows clearer evidence of knowledge and influence of the understanding of design. This is to be expected, since the shaping and reshaping, the summarising and condensing has taken place over time. Conference results and discourses are highly depended on the already available documentation. In this work, all other rules of discourse have been observed as well. Thus, it is evident that discourse design can be influenced through the speaker selection, their backgrounds and topics of presentations, as well as the time allocated to each. In this selection, the politics involved is always latent. In Chapter A.3.5, the discourse of the conferences as discursive as cases is validated. The outcome is very interesting, as it reveals statements that have and might influence not only the concept of design, but also its understanding. For instance, design thinking is the foundation of the discursive practice design. Such a design practice is marked by the shift towards a rhetoric and dialectic. Designers can solve design problems, such as creating a design theory, only through conversations. Designing design aimed at conceptualising the future of design is designing based on rhetoric and dialectic, because the base is text and conversation with the actors in the network—the community of individuals who come together in order to solve some design problems. It is important to note that, designing in a conference setting, as presented in the three cases, is participatory. In such instances, design is a social process, as the design activity extends beyond one designer. When engaged in a participatory design workshop, the attendees are an integral part of the social process of design. Moreover, they play an active role in the issue/problem raising, discussion and decision-making processes that are part of the early design stages of a project. When such an approach is adopted, the boundary between designers and users becomes blurred (Luck 2003, p.523). Reflecting on what was previous stated in Chapter 3.7, various social practices are recognized, namely (1) the way we are doing a job—i.e., using language; (2) discourse serves as representation and re-contextualisation of other practices to incorporate them into their own; and (3) discourse helps in the constitution of identities (Fairclough 2000). When discussing these events, it is possible to apply discourse analysis, adopting discursive methods to design theory. However, discourse should not be seen as the hammer that treats everything as a nail, since ‘…there exists no strictly Foucauldian method of analyzing discourse’ (Hook 2001, p.521). In other words, when the aim of an event is generating a discursive designing process, it should not be governed by strict rules. For instance, we can see the entire process of discursive designing from an action theory perspective, as was shown in Chapter 3.8. All criteria can be applied, since action research is a group activity with an explicit critical value basis and is founded on a partnership between action researchers and participants, all of whom are involved in the change process. The participatory process is educative and empowering, involving a dynamic approach in which problem identification, planning, action and evaluation are interlinked. When such approach is adopted, knowledge may be advanced through reflection and research, and qualitative and quantitative research methods may be employed to collect the data. Different types of knowledge, including practical and prepositional, may be produced by action research. Theory may be generated and refined, and its general application explored through the cycles of the action research processes. Yet, it also highlights presence of differences, since not all participants have been invited to consciously design theory in an action research process. The action research frame also demonstrates the value of the process applied, allowing and framework of the designing design theory to be better understood. The discursive design theory process—designing design—can also be framed as grounded theory (Chapter A.3.9). In social research, generating theory goes hand in hand with verifying it (Glaser and Strauss 1967, p.2). It is a systematic inquiry to construct theory (Bryant 2010). This is succinctly explained by Hannafin (1997), who noted: ‘theory-based approaches provide designers with powerful heuristics that guide design processes and procedures rather than provide explicit prescriptions’ (p.102). Developing a theory that can be applied to elucidate the shaping of the understanding of the notion of design and applying this theory in order to reshape the understanding of design is a grounded theory process, whereby theory merges into practice. ‘It assists designers in synthesizing across, as well as recognizing important distinctions among, various theoretical perspectives’ (Ibid, p.102). As Hannafin (1997) ponted out: Finally, grounded designs and their frameworks are validated iteratively through successive implementation. Methods are proven effective in ways that support the theoretical framework upon which they are based, and the framework itself is refined as implementation clarifies or extends the approach. The design processes and methods continuously inform, test, validate, or contradict the theoretical framework and assumptions upon which they were based, and vice-versa. (p.103) Therefore, it can be said that discursive design theory in action—Designing Design—is a grounded design process. While all the conditions are met, Hannafin (1997) cautioned that we need to be aware that ‘Clearly, not all design practice is grounded’ (p.103). We should also be mindful that the discursive designing practice was not intended to be grounded. Within the circular process of designing the research, discussed in Chapter A.4 to A.9, further defining and contextualising the process of designing design helps with generating and exploring the discourse and stating the theory. In A.4, a history of designing design is presented, highlighting some rudimentary statements of relevance for this study (Jonas 1996) which puts it into the context of Universality. In the view of Giaccardi (2005), designing design as a meta design concept, as it is a design by anticipation. Glanville (1999) described a process of simplification and pattern finding to develop our understandings. Glanville argued that design is a process of continuous modification and unification—the inclusion of an increasing number of elements into a coherent whole. It may also involve an occasional re-start, extension, and revolution, as well as the increase in range and of simplification. When designing design, theory designing can be accomplished in different ways, as was shown in Chapter A.5. While it can be achieved through externalisation within a group process, it can also be an individual process (conferences and text-based individual patterning). However, while the designing of theory has to be based on some clear conditions, it can also be seen as a basic human activity (Chapter A.6.) Everybody designs; design is not a monopoly of designers (Rittel 1988). Each iterative process that changes existing situations can be referred to as design. Based on this premise, design is not an exclusive profession, since many professions include processes based on iterations and changes of existing situations. Still, there is a difference between professional designers and non-designers because a ‘reflective practice approach to design engages in knowing-in-action that serves as a substantial base of design skills’ (Wakkary 2005, p.1). This definition leaves only the explicit knowledge in the realm of the design profession and indicates the need for a design theory designer, a design theory specialist. As shown in Chapter A.7, Designing Design is driven by design thinking which should be viewed as an instance in a discursive practice reaching the goal. It is thus a technique, developed based on the understanding of what is needed for the production, as well as the consequences of such a theory and model. Design thinking is about the dependencies and the acceptance of such a theory within the community of professionals, within the design theory community. Designing of design (theory) is also designing a system, since all systems comprise several components, which are interdependent and interact with each other to form an integrated whole within a specific context. This is exemplified in the design theory developed in this thesis. The interdependent group of statements is thus organised to form the systemic whole. As the observer is the one that decides what belongs to the system, not only the system space, but also the designing design theory space and its boundaries, changes with the research process and statements produced within the discursive system. This is presented in Chapter A.6−A.9, which also define the system boundary, while also ensuring viability of this approach by limiting input to the discourse system. In Chapter A.9 and A 9.1, the discursive theory design is put into an epistemological context. In this process, it is assumed that designing design does not solve finite problems, as it creates new

Activities of the Institute for Computer Applications in Science and Engineering

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April 1, 1985 through October 2, 1985 is summarized

UNSTABLE TERRITORIES OF REPRESENTATION: Architectural Experience and the Behaviour of Forms, Spaces and the Collective Dynamic Environment

This thesis applies an interdisciplinary cybernetic and phenomenological analysis to contemporary theories of representation and interpretation of architecture, resulting in a speculative theoretical model of architectural experience as a behavioural system. The methodological model adopted for this research defines the main structure of the thesis where the narrative and the contributing parts of its complexity emerge. The narrative is presented through objectives and hypotheses that shift and slide between architectural representation and its experience based on three key internal components in architecture: the architectural forms and spaces, the active observers that interact with their environment, and finally, the responsive environment. Three interrelated research questions are considered. The first seeks to define the influence of the theoretical instability between complex life processes, emerging technologies and active perception upon architecture. The second questions the way in which the architectural experience is generated. The third asks: Does architecture behave? And if so, is it possible to define its behavioural characteristics related to its representation, experience and the medium of communication in-between? The thesis begins by exploring the effect of developments in digitally interactive, biological, and hybrid technologies on representation in architecture. An account of architectural examples considers the shift in the meaning of representation in architecture from the actual and literal to the more conceptual and experimental, from the individual human body and its relations to the multifaceted ecosystem of collective and connected cultures. The writings of Kester Rattenbury, Neil Leach, and Peter Cook among others contribute to the transformation of the ordinary perceptual experience of architecture, the development of experimental practices in architectural theory, and the dynamism of our perception. The thesis goes on to suggest that instability in architectural representation does not only depend on the internal components of the architectural system but also on the principles and processes of complex systems as well as changes in active perception and our consciousness that act as the external influences on the system. Established theoretical endeavours in biology of D’Arcy Thompson, Alan Turing, and John Holland and philosophies of Merleau-Ponty, Richard Gregory, and Deleuze and Guattari are discussed in this context. Pre-programmed and computational models, illustrative and generative, are presented throughout the thesis. In the final stage of the development of the thesis architecture is analysed as a system. This is not an unprecedented notion, however defining the main elements and components of this system and their interactions and thereafter identifying that the system behaves and defining its behavioural characteristics, adds to the knowledge in the field of theoretical and experimental architecture. This thesis considers the behavioural characteristics of architecture to be derived from the hypothetical links and unstable thresholds of its non-dualistic notions of materiality and immateriality, reality and virtuality, and finally, intentionality and interpretation

Enhancing numerical modelling efficiency for electromagnetic simulation of physical layer components.

The purpose of this thesis is to present solutions to overcome several key difficulties that limit the application of numerical modelling in communication cable design and analysis. In particular, specific limiting factors are that simulations are time consuming, and the process of comparison requires skill and is poorly defined and understood. When much of the process of design consists of optimisation of performance within a well defined domain, the use of artificial intelligence techniques may reduce or remove the need for human interaction in the design process. The automation of human processes allows round-the-clock operation at a faster throughput. Achieving a speedup would permit greater exploration of the possible designs, improving understanding of the domain. This thesis presents work that relates to three facets of the efficiency of numerical modelling: minimizing simulation execution time, controlling optimization processes and quantifying comparisons of results. These topics are of interest because simulation times for most problems of interest run into tens of hours. The design process for most systems being modelled may be considered an optimisation process in so far as the design is improved based upon a comparison of the test results with a specification. Development of software to automate this process permits the improvements to continue outside working hours, and produces decisions unaffected by the psychological state of a human operator. Improved performance of simulation tools would facilitate exploration of more variations on a design, which would improve understanding of the problem domain, promoting a virtuous circle of design. The minimization of execution time was achieved through the development of a Parallel TLM Solver which did not use specialized hardware or a dedicated network. Its design was novel because it was intended to operate on a network of heterogeneous machines in a manner which was fault tolerant, and included a means to reduce vulnerability of simulated data without encryption. Optimisation processes were controlled by genetic algorithms and particle swarm optimisation which were novel applications in communication cable design. The work extended the range of cable parameters, reducing conductor diameters for twisted pair cables, and reducing optical coverage of screens for a given shielding effectiveness. Work on the comparison of results introduced ―Colour maps‖ as a way of displaying three scalar variables over a two-dimensional surface, and comparisons were quantified by extending 1D Feature Selective Validation (FSV) to two dimensions, using an ellipse shaped filter, in such a way that it could be extended to higher dimensions. In so doing, some problems with FSV were detected, and suggestions for overcoming these presented: such as the special case of zero valued DC signals. A re-description of Feature Selective Validation, using Jacobians and tensors is proposed, in order to facilitate its implementation in higher dimensional spaces

Indexed dependence metadata and its applications in software performance optimisation

To achieve continued performance improvements, modern microprocessor design is tending to concentrate an increasing proportion of hardware on computation units with less automatic management of data movement and extraction of parallelism. As a result, architectures increasingly include multiple computation cores and complicated, software-managed memory hierarchies. Compilers have difficulty characterizing the behaviour of a kernel in a general enough manner to enable automatic generation of efficient code in any but the most straightforward of cases. We propose the concept of indexed dependence metadata to improve application development and mapping onto such architectures. The metadata represent both the iteration space of a kernel and the mapping of that iteration space from a given index to the set of data elements that iteration might use: thus the dependence metadata is indexed by the kernel’s iteration space. This explicit mapping allows the compiler or runtime to optimise the program more efficiently, and improves the program structure for the developer. We argue that this form of explicit interface specification reduces the need for premature, architecture-specific optimisation. It improves program portability, supports intercomponent optimisation and enables generation of efficient data movement code. We offer the following contributions: an introduction to the concept of indexed dependence metadata as a generalisation of stream programming, a demonstration of its advantages in a component programming system, the decoupled access/execute model for C++ programs, and how indexed dependence metadata might be used to improve the programming model for GPU-based designs. Our experimental results with prototype implementations show that indexed dependence metadata supports automatic synthesis of double-buffered data movement for the Cell processor and enables aggressive loop fusion optimisations in image processing, linear algebra and multigrid application case studies