A system for remote calculations called \Specialized web portal for solving problems on multiprocessor computing systems" has been developed and installed at the Department of Ill-Posed Problems of Analysis and Applications of the Institute of Mathematics and Mechanics UrB RAS. The parallel algorithms have been incorporated into this system to solve the inverse gravity problem of lateral density reconstruction, the structural inverse gravity and magnetic problem of the contact surfaces reconstruction, and solving SLAEs with block-tridiagonal matrices in geoelectrics problems.
The modern physics widely uses mathematical modeling for solving di erent problems. The solution of some problems is very complex process which requires the cutting-edge mathematics, as well as the highest level of computerization. Firstly, the solution of problems requires storage and processing of large amounts of data. Secondly, the algorithms have high complexity, i. e. increasing the input data size substantially increases the computation time. Solving this problems using a personal computer takes from several hours to several days. In this case the parallel computing can be a great aid. Using the multiprocessor systems or GPU's reduces the calculation times by several orders of magnitude.
On the other hand, the researcher has to face many challenges. He must be an expert in his subject area, and also must be a mathematician to use algorithms for solving complex equations. Implementation of these algorithms on modern parallel computing systems requires not only good programming skills but also knowledge of special technologies such as MPI or CUDA.
Apparently, getting scienti c results is a complex and time-consuming process which requires expensive human resources and powerful computing systems.
Thus, there is a need for a specialized web portal which would greatly
facilitate and reduce the cost of these processes. There are several solutions like [
The web portal [
The web portal consists of three major parts shown on Fig. 1: IIS HTTP server with a web application; MS SQL Server 2008 to store all user tasks with input and output data; a service to perform the data transfer, to launch tasks on various computers, to determine task status, and to transfer the results into the web portal. Web application is developed using C# and ASP.NET technology.
The user has to be registered in the system to create or to view tasks. To create a new task the user must choose a required task from the prepared list of available task types. Some of the parameters are de ned by the task type, such as grid size, desired accuracy and boundary conditions while the others are de ned by the computing system type, such as cores and nodes numbers and execution time limit. To launch a task the user must specify all required parameters, choose a computer type and upload the input les. The task data are stored in the database.
After launching his task the user can watch the progress in a separate page. The task is considered successfully completed when the program on a computing system nishes without errors and all output les are transferred to web server. The page for completed task shows the actual execution time and allows user to download the output les (Fig. 2). It also demonstrates images of output le created using Golden Software Surfer & Voxler or gnuplot graphics software.
The algorithm includes the following steps: 1. Look for a new task in database.
1.1. Read the task input parameters. 1.2. Validate the input les for proper format and structure. 1.3. Transfer the input les to the computing system. 1.4. Launch the task solving executable on the computing system. 1.5. Store the launched program id in the database. 2. Look for a launched task in database.
2.1. Check for a nished program on the computing system. 2.2. Transfer the output les to the web server. 2.3. Create an image of output les using graphics software. 2.4. Mark the task as nished.
The service uses SSH and SFTP protocols for remote interaction and le transfer. Currently the service supports interaction with remote computing systems with the Slurm Workload Manager. This system is widely used by supercomputers and computer clusters and it provides a framework for executing and monitoring programs for CPUs and GPUs. The service generates a batch script which transfers input data to the executable and launches it using the sbatch command. This command returns the task ID which is used to check for a nished program utilizing the sacct command.
After retrieving the output data from the remote system the service transfers it to the database and to graphics software. It launches a prepared script for Surfer or gnuplot which plots a preview of output les according to the task type. For example, for the structural inverse gravity problem of nding a contact surface, the result would be a 3D surface plot created by Surfer. 3
Currently, the specialized web portal can be used to perform tasks for solving
gravity problems ( nding a lateral density, reconstruction the contact surfaces),
magnetic problems (reconstruction the contact surfaces), eld separation by
depth problem and solve SLAEs with block-tridiagonal [
The problem of separating gravity or magnetic elds by depth is solved using
the technique by P. S. Martyshko & I. L. Pritkin [
This technique consists of several steps. The rst is to exclude side sources of
eld. To do this we must nd the solution of Dirichlet problem in the considered
area and subtract it from the original eld. The portal uses the parallel algorithm
based on the separation of variables method [
The problem of nding a variable density in a horizontal layer is described by a linear two-dimensional Fredholm integral equation of the rst kind: A =f
Z1Z1( 1 1 p(x
1 p(x where f is the gravitational constant, g(x; y) is the known gravitational eld, and (x0; y0) is the desired density distribution function.
After the discretization into n = M N grid of the area D = f(x; y) : a 6 x 6 b; c 6 y 6 dg and approximation of the integral operator A using quadrature rules, it takes the form xi)2 + (yu yj )2 + H12 (i 1)M+j x y = b(v 1)M+u; (1) A
M M ( = f X X The gravity and magnetic problems of reconstruction of the contact surfaces are described by the nonolinear two-dimensional Fredholm integral equations of the rst kind:
) where f is the gravitational constand, g(x0; y0; 0) is the known gravitational eld, Z(x0; y0; 0) is the known magnetic eld, and (x; y) is the function which describes the desired surface.
After the discretization into n = M N grid of the area D = f(x; y) : a 6 x 6 b; c 6 y 6 dg and approximation of the integral operators A or B using quadrature rules, this equations take the form:
A[z] = F :
This equation is solved by the componentwize Newton method [
Each algorithm has to be researched and tested on di erent types of data before implementing to the system.
Now the authors are developing modules for solving problems of nding several contact surfaces simultaneously by the total gravitational eld and magnetic problem of nding the contact surface in the case of an arbitrary magnetization direction.
The problem of constructing the schedule for trains on the single-track railway will be incorporated soon.
The test version of the web portal currently works with the Uran supercomputer of the Institute of Mathematics and Mechanics. It allows to run task on the multicore Intel Xeon processors or NVIDIA Tesla GPUs.