Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures

A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational efficiency for large multidimensional computations on standard architectures such as powerful workstations. However, the data structure of the original implementation, based on trees of pointers, provides limited opportunities for efficiency enhancements, while posing serious challenges in terms of parallel programming and load balancing. The present contribution proposes a new implementation of the whole set of numerical methods including Radau5 and ROCK4, relying on a fully different data structure together with the use of a specific library, TBB, for shared-memory, task-based parallelism with work-stealing. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions on multi-core and many-core architectures, demonstrating high scalability

Format Abstraction for Sparse Tensor Algebra Compilers

This paper shows how to build a sparse tensor algebra compiler that is agnostic to tensor formats (data layouts). We develop an interface that describes formats in terms of their capabilities and properties, and show how to build a modular code generator where new formats can be added as plugins. We then describe six implementations of the interface that compose to form the dense, CSR/CSF, COO, DIA, ELL, and HASH tensor formats and countless variants thereof. With these implementations at hand, our code generator can generate code to compute any tensor algebra expression on any combination of the aforementioned formats. To demonstrate our technique, we have implemented it in the taco tensor algebra compiler. Our modular code generator design makes it simple to add support for new tensor formats, and the performance of the generated code is competitive with hand-optimized implementations. Furthermore, by extending taco to support a wider range of formats specialized for different application and data characteristics, we can improve end-user application performance. For example, if input data is provided in the COO format, our technique allows computing a single matrix-vector multiplication directly with the data in COO, which is up to 3.6$\times$ faster than by first converting the data to CSR.Comment: Presented at OOPSLA 201

Julia: A Fresh Approach to Numerical Computing

Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia questions notions generally held as "laws of nature" by practitioners of numerical computing: 1. High-level dynamic programs have to be slow. 2. One must prototype in one language and then rewrite in another language for speed or deployment, and 3. There are parts of a system for the programmer, and other parts best left untouched as they are built by the experts. We introduce the Julia programming language and its design --- a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, what good computation is really about, recognizes what remains the same after differences are stripped away. Abstractions in mathematics are captured as code through another technique from computer science, generic programming. Julia shows that one can have machine performance without sacrificing human convenience.Comment: 37 page

Study and Performance Analysis of Different Techniques for Computing Data Cubes

Data is an integrated form of observable and recordable facts in operational or transactional systems in the data warehouse. Usually, data warehouse stores aggregated and historical data in multi-dimensional schemas. Data only have value to end-users when it is formulated and represented as information. And Information is a composed collection of facts for decision making. Cube computation is the most efficient way for answering this decision making queries and retrieve information from data. Online Analytical Process (OLAP) used in this purpose of the cube computation. There are two types of OLAP: Relational Online Analytical Processing (ROLAP) and Multidimensional Online Analytical Processing (MOLAP). This research worked on ROLAP and MOLAP and then compare both methods to find out the computation times by the data volume. Generally, a large data warehouse produces an extensive output, and it takes a larger space with a huge amount of empty data cells. To solve this problem, data compression is inevitable. Therefore, Compressed Row Storage (CRS) is applied to reduce empty cell overhead

Study and Performance Analysis of Different Techniques for Computing Data Cubes

Data is an integrated form of observable and recordable facts in operational or transactional systems in the data warehouse. Usually, data warehouse stores aggregated and historical data in multi-dimensional schemas. Data only have value to end-users when it is formulated and represented as information. And Information is a composed collection of facts for decision making. Cube computation is the most efficient way for answering this decision making queries and retrieve information from data. Online Analytical Process (OLAP) used in this purpose of the cube computation. There are two types of OLAP: Relational Online Analytical Processing (ROLAP) and Multidimensional Online Analytical Processing (MOLAP). This research worked on ROLAP and MOLAP and then compare both methods to find out the computation times by the data volume. Generally, a large data warehouse produces an extensive output, and it takes a larger space with a huge amount of empty data cells. To solve this problem, data compression is inevitable. Therefore, Compressed Row Storage (CRS) is applied to reduce empty cell overhead