Numerical simulation of natural phenomena is being fostered by recent advances in powerful high processing computing platforms. Scientists in various areas, such as human cardiovascular system, model a phenomenon being studied through a set of mathematical equations. As scientists strive to obtain a more realistic simulation, a huge amount of data is produced. Unfortunately, there has been little work on supporting numerical simulation data management, which leaves simulation scientists with huge standard text les and complex analytical programs that eventually extract some meaningful information to validate scienti c hypotheses. Moreover, some analytical queries cannot, as well, be represented using none of the scienti c query languages. In this context, this paper tries to bridge this gap by raising some issues involved in numerical simulation data analysis. A representation for numerical simulation data is presented that considers a multidimensional model, for dimensional variables, and their corresponding physical quantities. A cloud service to interface with the numerical simulation data manager is proposed and its integration with the Neblina cloud middleware is explored.
Many scienti c areas are taking advantage of development in high processing computing to model natural phenomena through in-silico simulation. The process involved in modeling phenomena starts by observing phenomenon data, and modeling the process through a set of mathematical di erential equations that expresses the variation of selected physical quantities on time-space. Next, the scientist may choose an appropriate numerical method that would solve the equations and compute for each reference point the values for selected physical quantities. Using state-of-art cluster platforms computer scientists strive to obtain the most possible realistic simulations to compute weather forecasts, just to name an application.
In this paper we propose a novel strategy for scienti c simulation data
management based on database approach. We focus on the support to the analysis
of simulation results, taking a sample of a simulation output and loading it onto
a cloud data service modeled using a multi-dimensional array representation for
space and time to manage space-time multi-scale dependent data. We illustrate
our discussion with the simulation of the human cardiovascular system developed
at LNCC, INCT-MACC [
Recent studies have demonstrated the need for a more e cient storage, indexing
and processing strategies for scienti c data [
In Ogasawara [
The storage of numerical simulation data has been investigated by [
Another important initiative in support for scienti c data management is
SciDB [
Considering the analysis of simulation data, one question is to determine the
past and future cone of information, as presented by Sowa [
The Magellan project [
As discussed in section 1, we are interested in specifying a data management service in support to numerical simulation results analysis. This section investigates some possible representations for numeric simulation data and how to extend database functionality to support scienti c data handling under it. 3.1
Simulation data can be interpreted as composed by two sets of variables: dimensional and physical quantities. Typically, the dimensional variables include space and time. The space dimension refers to a mesh, which represents the topology of the physical domain as a composition of simple geometric objects. A mesh is represented by: a set of points, referring to the vertices of the geometric objects; the set of edges linking the points and the faces of the model. Observe, yet, that simulations may adopt di erent scales throughout the domain. Furthermore, given a physical quantity, its value in a reference coordinate may change through scales. A given simulation may be composed of data in di erent scales, according to the precision requirements in di erent parts of the physical domain.
Our rst e ort to represent numerical simulation data uses SciDB. A user
species multidimensional structures by providing the range values for each dimension
and a list of attribute values to compose a cell. In addition, a versioning
mechanism keeps historical values for each attribute. In this context, the following
mapping strategy has been de ned: for each set of physical quantities
corresponding to a phenomenon being simulated in a given scale; de ne the set of
dimensions; specify the list of physical quantities to be computed; create an
array having the dimensions as and attributes as . Using the AQL [
Through the AQL query language, we can use the following schema to represent 1D (i.e di erent scale) of the human cardiovascular system: CREATE ARRAY Geometry1D <velocity: double, pression: double, flow: double> [ simulations=0:*,1,0, t=0:500,500,0 ]
A 1D model represents each cross-section summarized in a single point. Thus, each point contains the values for the physical quantities on each time step. Additionally, It's refers to the di erent simulations over the same mesh. Observe that the array data model adopted by SciDB enables the direct representation of multidimensional objects produced in numerical simulations. 3.3
In order to support the analysis of numerical simulation output, algebraic operators must be provided, eg.: drill down through scales - given a reference coordinate in scale si, return the corresponding set of points in scale sj; AQL and AFL languages do not have su cient mechanisms to support many analytical queries. The challenge is to create new operations and functions to bridge this gap, as well as, to coupling them to algebraic operators. An example is to obtain the values for pression where the highest values are achieved: aggregate(Geometry3D, max(pression)); 3.4
From an architectural point of view, we expect to develop a service to interface with the solvers - producing simulation data - and with scientists - submitting analytical queries to the system. The Simulation Data Management Service (SDMS) is responsible for providing such an interface as a cloud service, and should manage the storage and retrieval of the simulation data making it transparent to scienti c applications. The availability of the SDMS as a cloud service fosters the collaborative use of simulation data among scientists of a same research project and among di erent projects.
An important aspect of the cloud service approach is the possibility to
explore elasticity [
Regarding the SDMS, an important issue is the research and development of
mechanisms that would enable its deployment in a private cloud as a Service
(SaaS) [
The SDMS has been integrated into Neblina. This integration makes the cloud environment transparent to SDMS, enabling for instance the activation of its services. In Fig. 2 the architecture of the integrated environment is shown and the numbers suggest a retrieving order. 4
We investigate the requirements involved in designing a data management service in support for numerical simulation analysis. A multidimensional modeling approach represents the dimensions used in referencing each individual simulation point, and maps each point to its respective physical quantity values. We observe that although the multi-array model adopted by SciDB enables the implementation of the multidimensional representation, further extensions are required to fully support numerical data representation and analysis requirements. In particular, some analysis may require physical quantities to be computed over di erent abstractions, such as computing their values in a face or edge of a geometry object in a mesh. Moreover, supporting modeling through di erent scales would require a relationship between multiple representations of the same multidimensional space-time. Some proposed analytical queries can not, as well, be represented using none of the SciDB query languages. New functions and user data types would be needed to cope with those. We expect that this work will provide a better understanding concerning the needs involved in analytical data management for multidimensional numerical simulations.