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APPROACH TO NUMERICAL SOLUTION OF EM PROBLEMS 459

If so, we can apply the LEGO decomposition
cutting the computation domain into
subdomains like Figure 9.2.2 illustrates and
sending each subdomain for a numerical
update to an independent processor. As soon
as all processors finish their task, they
transfer their field data to the core processor
that reconciles and updates the received E-
Figure 9.2.2 Cube subdivided into smaller and H-fields through the boundary
subdomains
conditions on the adjacent edges or nodes.

9.2.3 Parallel Processing

The parallel processing is the equivalent of LEGO decomposition when a numerical algorithm
can be fragmented. Then each of independent parts is executed simultaneously on different
processors attached to the same or multiple computers connected by a network. Such network
of working in parallel computers forms one HPC with hundreds or thousands of processors and
shared memory. The computer
can be independent developing a
Data Local
processor 1 memory 1 distributed system that can run
multiple tasks simultaneously or
Data Local a single HPC with multiple
processor 2 memory 2
Main Control processors solving a single
memory unit problem. It makes no real
differences for the user because
Data Local it appears like a single computer
processor n memory n
and interface in both cases. The
following material is just a very
brief synopsis. More details can

Figure 9.2.2a Block-diagram of SIMD system be found in the specialized
literature [3, 10]. Keep in mind
that this area is extremely dynamic and literally changes every hour if not a minute. The block
diagram of a computer system with Single Instruction stream and Multiple Data streams
(SIMD) typical for single HPC is illustrated schematically in Figure 9.2.2a . In this system,
17
the initial data and instructions how to execute the program come from the common control
unit to each data processor. The results of each data processing go back and forth to local and
main memory until the simulation process is finished. The procedure of such exchange is
managed by the control unit. As any centralized structures, SIMD has several drawbacks like
not all algorithms can be parallelized easily, difficult to synchronize and optimize the data
transfer between processors and main memory, etc. The best results could be reached if the
execution time of programs in all processors is the same or very close. Only then, the processors
do not mutually delay their actions [10].

17 Public Domain Image, source: https://edux.pjwstk.edu.pl/mat/264/lec/index121.html. We used some
text information from this website too.