Intelligent and Distributed Solving of Multiphysics Problems

Coordinated by Software Agents

An Intelligent Approach for Decentralized Simulations

Desirée Vögeli

, Sebastian Grabmaier

, Matthias Jüttner

, Michael Weyrich

Peter Göhner

and Wolfgang M. Rucker

Institute of Industrial Automation and Software Engineering, University of Stuttgart,

Pfaffenwaldring 47, 70569 Stuttgart, Germany

Institute for Theory of Electrical Engineering, University of Stuttgart, Pfaffenwaldring 47, 70569 Stuttgart, Germany

Keywords: Multiphysics Simulation, Software Agent, Distributed System, Case-based Reasoning.

Abstract: This paper presents an intelligent approach to support engineers with performing computational simulation

of new developments and prototypes. With multiple interacting physical effects and large three dimensional

models the choice of the right solution strategy is crucial for a correct solution and an acceptable calculation

time. The presented multi-agent system can solve these simulation tasks using distributed heterogeneous

computation resources with the objective to reduce the calculation time. An important factor for the criterion

time is the choice of the linear solver. Here a case-based reasoning concept is introduced to improve the

decisions in the multi-agent system. Allowing each agent to solve its problem part by using appropriate

solution methods, a decentralized architecture with autonomous software agents is provided.

1 INTRODUCTION

Nowadays, our daily life becomes more and more

affected by intelligent assistance systems. Industrial

automation systems interact with each other to build

individual products (Jazdi, 2014), kitchen devices are

communicating with each other (Blasco et al., 2014),

and cars are driving autonomously (Zhang et al.,

2016). These things assist their users based on

improving automation technology. Even if the things

are built and run automatically, their development

must be done by an engineer.

In times of workforce deficits in the engineering

domain and an ever shorter time to market, engineers

have to manage many tasks. When developing a new

system, they have to check different approaches. Due

to missing time decide must be based on their

experiential knowledge. This results in missing better

solutions. Therefore, they need support in form of

software tools and assistance systems. Up to now

there are only a few assistance systems to support the

development processes of systems by creating new

solutions on their own. One of these is Depias (Beyer

et al., 2016). It allows an engineer to plan a logistic

system, finding different possible compositions, and

comparing them. Other concepts deliver methods to

generate code from models (Mozumdar et al., 2008)

or to automatically manage system requirements

(Lambersky, 2012). None of these approaches can be

used to develop a whole system yet, but they support

partially the engineering process. Another part of the

development process that is becoming more and more

important are simulations (Clement et al., 2017).

Simulations are used to analyze, optimize, and

understand system behaviors. They are also able to

assist at virtual commissioning and test verification.

An important type of simulations are so-called

multiphysics simulations for which different tools

exist. However most simulation tools are made for

single physics problems. All these tools need a huge

amount of computing power and time plus expertise.

These multiphysics problems become even bigger

due to the necessity of more detailed simulations.

Hence the systems become more complex and the

environment has to be considered (Tolk, 2016). That

is why this paper shows an approach of how to solve

200

Vögeli, D., Grabmaier, S., Jüttner, M., Weyrich, M., Göhner, P. and Rucker, W.

Intelligent and Distributed Solving of Multiphysics Problems Coordinated by Software Agents - An Intelligent Approach for Decentralized Simulations.

DOI: 10.5220/0006590402000207

In Proceedings of the 10th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2018) - Volume 1, pages 200-207

ISBN: 978-989-758-275-2

multiphysics problems in parallel using software

agents inspired by the contract net protocol.

After the motivation and the introduction, chapter

2 describes multiphysics simulation and existing

approaches for parallelization. Afterwards

possibilities to decompose multiphysics problems are

given. The last part of chapter 2 introduces the

software agents and the concept to simulate the parts

in parallel. The procedure of this agent-based system

is shown in chapter 3 using an example. In chapter 4

a concept to improve the effectivity of the decisions

within the multi-agent system using case-based

reasoning is presented. Finally a conclusion and an

outlook are given in chapter 5.

2 DECOMPOSITION OF

MULTIPHYSICS PROBLEMS

FOR PARALLEL SIMULATION

To simulate multiphysics problems in a decentralized

way an approach to decompose the problem is

introduced. Therefore an introduction to multiphysics

simulation is given before the flexible and self-

organizing agent concept is presented.

2.1 Multiphysics Simulation

A multiphysics simulation analyzes relations between

different domains and their effects among

themselves. This is getting more and more important,

since model driven engineering and virtual

commissioning are significant topics today (Boschert

and Rosen, 2016). This simulations are used to

predict and to understand the behavior of a system,

often before building it. Thus a geometrical model of

the system is built. The included physical laws are

represented by partial differential equations or

integral equations. To simulate physical effects, the

model is discretized using e.g. the finite element

method (FEM) or the boundary element method

(BEM) (Gupta, 2002). Software tools such as

COMSOL Multiphysics (Dickinson et al., 2014) are

used. For solving the resulting linear equation system

different solvers exists. Some use direct methods and

others iterative ones. Direct methods mount the

matrix by a sequence of calculation steps. In iterative

methods, the results will be approximated until the

convergence criterion is reached.

To estimate which configuration is better suited

for a simulation task, experiential knowledge is

needed. And even then it is often impossible to

predict the best configuration before the simulation.

There are solvers that deliver for nearly every task a

simulation result and others that are good for only a

few ones but do these simulation in just a fraction of

time with less computational effort.

In order to meet the increasingly larger and more

complex models, the computational effort can be

spread over several distributed computers. Next to

classical high performance computing on a

supercomputer, there are other approaches to run

simulations in parallel on distributed heterogeneous

computing resources. In many approaches there is a

static decomposition before the simulation or the

simulation tool is made for exactly this use case. So

each one can just be used for very specific problem

setups. To solve different kinds of multiphysics

simulations in parallel, there must be a more general

attempt to decompose a multiphysics problem. A

more general approach is presented in (Vázquez et al.,

2016). The code Alya works on already discretized

models. But here, every partial problem must have the

same discretization and is calculated with the same

code. As computing resource a super computer is

used, but super computers are expensive.

However, if a model is updated in the presented

approaches, for example by adding a new physical

domain, everything must be simulated again and the

configuration must be updated, too. That is why in

this paper a more flexible approach is introduced,

which uses idle and already existing personal

computers (PC) and servers.

2.2 Decomposition of Multiphysics

Problems

With the decomposition of multiphysics problems,

there are two goals that should be reached. The first

goal is to enable calculation resources with less

calculation power to assist in the distributed

simulation process, for example if they don’t have

enough memory to load the problem or if they just

have the ability to simulate parts like the heat transfer

but not electromagnetic waves. The second goal is to

use different methods to get a better result in shorter

time. In some cases it can be an opportunity to

simulate different areas or different physical effects

with different methods and configurations (Buchau et

al., 2003; Fetzer et al., 1999). Some approaches to

decompose a problem for distributed calculation is

shown in Figure 1.

To reduce the computational effort for one

resource, there is the possibility to simulate the

physical effects separately. This works on most

weakly coupled problems. Another possibility to

reduce the computational effort is to cut the model in

Intelligent and Distributed Solving of Multiphysics Problems Coordinated by Software Agents - An Intelligent Approach for Decentralized

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201

parts. To reduce the calculation time various

simulation configuration like the solver or the method

(FEM, BEM) can be evaluated.

Figure 1: Objectives and approaches for decomposition of

multiphysics simulation problems.

When no coupling between the physical effects

exists, parallel calculation is trivial. Considering uni-

or bidirectional coupling between the physics,

information must be exchanged during the

simulation. For this exchange an intelligent resource

management is needed. One approach for this are

agent-based systems.

2.3 Agent-based Concept for a

Distributed System

To simulate the coupled problem parts on distributed

calculation resources software agents are used to

manage the solution process. Software agents are

autonomous software units able to interact with the

environment and communicate with each

other (Jennings and Wooldridge, 1996). The ability to

communicate is used to exchange information

between coupled problem parts. Therefore, the agents

use an agent communication language (ACL) based

on the guidelines of the Foundation for Intelligent

Physical Agents (FIPA, 2002). The ACL is based on

the human speech act and allows to structure

conversations. So, there is the possibility to add in

addition to an identifier a performative to a message,

such as INFORM, PROPOSE, AGREE, and many

others.

To manage the solving process next to an agent

management system (AMS) that cares for the

message transport and the directory facilitator (DF) as

yellow pages, three kinds of agents are developed: a

coordination, a calculation and a report agent. The

report agent that provides state news from all agents

received by messages isn’t regarded in the further

paper because it isn’t necessary for the calculations.

2.3.1 Coordination Agent

In the multi-agent system (MAS) there is one

coordination agent that manages the simulation

process. It gets the simulation task from the user and

informs the other agents about the new model and the

decomposition possibilities. It also supervises the

distribution process among the agents and decides

about the offers made by the calculation agents. With

the coordination agent’s graphical user interface, it is

possible to stop simulations or to update the model.

This can be used to integrate another physical effect.

2.3.2 Calculation Agent

The MAS contains many calculation agents. The

calculation agents have the task to do the partial

simulations. Thus they have the knowledge of the

necessary steps to simulate a model. A calculation

agent can have different abilities depending on the

calculation resource on which it runs and the

simulation software that is installed. Based on these

abilities they bid for the part problems they want to

simulate. Additional and redundant calculations are

also supported to speed up the process. As soon as a

calculation agent received the confirmation to a

partial problem it starts the calculation using various

software packages. To guarantee global convergence,

which means the fulfillment of all constraints rising

from couplings between partial problems, it

exchanges results with other agents involved.

Relevant results from other agents are considered in

their own solutions. If the local convergence criterion

is reached and no changes in the relevant results

occur, the partial problem is terminated. When all

partial problems are terminated, the global solution is

completed. The calculation agents also provide

interim results and the result to the user.

3 AN EXAMPLE ON

DISTRIBUTED AGENT-BASED

SIMULATION

In this chapter the solving procedure of the prototype

is illustrated using a realistic example. The prototype

implements the agents using the framework JADE

(Java Agent Developing framework) (Bellifemine et

al., 2007). Next to the presented agents in chapter 2.4,

an AMS and a DF are used. As bidirectional coupled

multiphysics problem microwave and dielectric

same

material

attributes

heat

transfer

direct FEM

same

physical

effects

decomposition

goal: get results in less time

goal: reduce calculation

capabilities for one resource

electro-

magnetic

waves

electric

current

iterative BEM

examples

approaches

area

distribution

physical

effects

distribution

solver

configuration

methods

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

202

heating is used for demonstration. Here a lossy

dielectric medium (water) in a waveguide is

considered. Hence the time harmonic electromagnetic

wave equation (EMW) and the heat transfer (HT) are

regarded. The underlying system of differential

equations is given by

    





 









 







    











with the electric field 





, the electric current density 



the temperature field T, the angular frequency ω, and

the thermal conductivity κ. Taking temperature

dependent conductivity  and permittivity 



into

account the wave number  reads





 











 















With the vacuum permeability 



and the vacuum

permittivity 



To simulate the problem three calculation

resources are used, listed in table 1. The data

exchange between the calculation resources uses

LAN technology. The access to the simulation tools

is realized by a Java interface.

Table 1: Available calculation resources.

PC 1

PC 2

PC 3

16 GB RAM

8 GB RAM

Intel® Core™

i7-3520M CPU

@ 2.90 GHz

Intel® Core™

i5 CPU 650 @

3.20 GHz

Intel® Core™

i5 CPU 650 @

3.20 GHz

tool for EMW

tool for HT

There are three phases for the MAS that are

explained in the next sub-sections: initialization,

decomposition, and solving.

3.1 Initialization Phase

First, all agents must be started. Each PC runs one

calculation agent (CalcA). PC 3 also runs the AMS,

the DF, and the coordination agent (CoordA). After

starting, the CoordA connects with the software tool.

The CoordA registers at the DF and starts the GUI,

where the user can load a model. The CalcAs CA1,

CA2, and CA3 on PC 1, PC 2, and PC3 connect with

the software tools. Then they check the performance

of their resource and register at the DF. Last the

CalcAs look for the CoordA using the DF and

subscribe, so that they will be informed when a new

model is available. After this initialization phase is

done, the MAS waits for the user to load a model.

3.2 Decomposition Phase

The goal of the decomposition phase is to manage the

decomposition of a model and to distribute the parts

to the system resources. The necessary

communication between the agents for the example

based on a dynamic allocation negotiation is shown

in Figure 2. As soon as the user loads a new model,

the coordination agent analyses it on splitting

possibilities and informs the CalcAs that have

subscribed. Now all agents aim to find the best

allocation of the problem parts. To get an overview of

the different problem parts, the CalcAs request a price

list from the CoordA that contains the parts and the

current biddings. Next the CalcAs have to make their

decision on which part to bid depending on their

abilities. The better the calculation power of a

resource, the more money the agent has to bid on

parts. Also dynamic abilities like utilization are

considered. The CoordA checks the biddings and

updates the price list if there is a higher bidding. It

also informs the formerly highest bidder and the new

highest bidder about the new list. As soon as an agent

has its problem part it starts calculating.

In this example the CA3 bids on the HT problem

part. The other two CalcAs both bid on the EMW

problem part. Therefore, they are overbidding each

other as long as the one with the better resource gets

the problem. However, the other agent is simulating

the EMW part with other simulation configuration

and tries to provide the result faster.

With this procedure the most promising variants

are computed on the best calculation resources. The

phase is finished when all problem parts are allocated.

If a model becomes updated, the new part is allocated

the same way to the CalcAs.

3.3 Solving Phase

During the solving phase the agents simulate their

partial problems. To take care of dependencies, the

agents cooperate with each other. So the first step of

this phase is, that every calculation agent informs all

others about the start of its task. Then the calculation

agents analyze which other problem part depends on

their own one. Next they subscribe to the calculation

agents that simulate the related parts. Here, the agent

with the HT problem part is interested in all results

about the EMW and the agents with the EMW

problem parts are interested in the HT part. After the

subscription, the agents start the calculations.

Intelligent and Distributed Solving of Multiphysics Problems Coordinated by Software Agents - An Intelligent Approach for Decentralized

Simulations

203

Figure 2: Communication during the decomposition phase.

Because of the lack of a stationary heat source in

the HT model, CA3 finishes soon and waits for results

from the EMW part to incorporate them as Joule’s

losses. When the first agent with the EMW problem

finds a result, it checks if the tolerances are within the

limits and if the result is already published. Here, it

isn’t published yet, so it sends a message with the

result information to the other agents. The other

agents check if their partial problem depends on the

results. Here CA3 requests the solution, since the

temperature depends on the heat sources. Before

publishing results that correspond to the convergence

criterion, the agents check, if they aren’t already

published. If so, they don’t publish them and just wait

for further results that may change something within

their own simulation. Once the convergence criterion

is reached and no agent is calculating anymore, the

simulation process is finished.

During the calculations, the user is able to add

further physical effects or couplings between them

into the simulation. When doing so the existing

solutions are reused as initial values.

3.4 The Solution

The graphic diagrams in figure 3 shows the

simulation results for the electromagnetic wave and

the heat transfer in the water. The solutions are

presented by the agents, using a browser as graphic

interface.

Besides the decomposition based on physical

domains, the introduced MAS is able to decompose

the simulation task based on geometries. It is also able

to use different software tools and numerical methods

to get a good result (Grabmaier et al., 2016; Jüttner et

al., 2017). Further decomposition in space and time is

possible.

The decision, which solver configuration has to be

chosen if there is more than one resource capable to

simulate it, is made by the calculation agents based

on heuristics. Experienced engineers are able to

choose a suitable solver configuration by regarding

the model and the study. To imitate this human

behavior, our MAS is expanded to learn from solved

cases. Therefore a case-based reasoning approach is

used.

Figure 3: Simulation results of the calculation agents: Top

electric field strength on the surface of the waveguide,

Bottom left temperature inside the dielectric media, Bottom

right Joules losses inside the dielectric media.

4 USING CASE-BASED

REASONING TO IMPROVE

THE EFFICIENCY

Case-based reasoning (de Mantaras, 2001) is used in

the field of automated reasoning to use similar cases

that are already solved to adapt the solution instead of

building a new one from scratch. The case-based

reasoning process is divided into four steps:

• Retrieve: the new task is compared with the

already solved tasks to find a similar one

coordination

agent

CA3 (HT

software)

CA2 (EMW

software)

CA1 (EMW

software)

INFORM: load-model

REQUEST: price-list

AGREE: price-list

PROPOSE: price-list

INFORM: price-list

loop

PROPOSE: price-list

INFORM: price-list

model

EMW

EMW in

the inside

HT in the

inside

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

204

• Reuse: the solution of the similar already

solved task is adapted for the current one

• Revise: the new solution based on the

adaption is valuated

• Retain: the new case with its task and

solution is saved to reuse it in the future

The advantage of this method compared with neural

networks is, that there is no need for an initial

training. Solutions can be created using the

conventional way, if there is no similar case that can

be adapted. Neural networks are set up by a training

data set while case-based reasoning approaches learn

from case to case due to the increasing database.

Thus, the algorithm used to compare the similarity

must be created by an expert. Here this method is used

to optimize the choice of the linear solver. Thus, the

cases are the simulation models with their studies and

the used solver configuration.

4.1 Cases

To learn from cases, these must be saved in a data

base. Therefore, a structure is needed. Figure 4 shows

the structure of the cases for multiphysics

simulations, consisting of model properties, approach

parameters, and a grading.

Figure 4: Structure of multiphysics simulation cases.

4.1.1 Model Properties for Comparison

To reuse information about the solving process from

already solved cases, there must be a possibility to

compare them. This is made by the model properties.

An important property is the discipline, like HT or

EMW in the previous example. Considering EMW

simulation many properties are evaluated, shown in

table 2. The parameters are grouped in boundary

conditions (BC), material properties (M),

discretization and geometry (G). The parameters are

represented by booleans, by integers or floats, and

others that contain lists. All information are a priori

available using the model description.

Table 2: Model properties from electromagnetic waves

problems.

property name

type

hasPortIntegral

boolean

hasPerfectlyMatchedLayers

boolean

isHermitian

boolean

maxGeometricalDistance

float

minGeometricalDistance

float

discretization

shapeOrder

integer

minSizeOfElements

float

maxSizeOfElements

float

minSkewness

float

averageSkewness

float

minQualityOfElementAngle

float

averageQualityOfElementAngle

float

averageElementsPerPenetrationDepth

float

minElementsPerPenetrationDepth

float

numberOfDegreeOfFredoms

integer

maxConductFact

float

waveNumber

array

maxImagWaveNumber

float

4.1.2 Approaches

To reuse the simulation configuration of already

calculated models, the information about how this old

cases were simulated must be saved. Here, the used

method, the software tool, and the solver

configuration are stored. The solvers have different

advantages and disadvantages, so there isn’t one that

is the best in any case (Meister, 2015). Some are slow

but solve the task in nearly any case, some are fast but

need much memory and some cannot even guarantee

to always find a solution. For the iterative applied

solvers there is also the choice of a suitable

preconditioner. The considered solver possibilities

for the electromagnetic wave physic are shown in

table 3.

Table 3: Considered solver configurations for simulation.

Solver

direct

MUMPS

Pardiso

Spooles

iterative

BiCGStab + left preconditioning

BiCGStab + right preconditioning

GMRES + left preconditioning

GMRES + right preconditioning

preconditioned CG

Since the solver choice doesn’t depend only on the

model properties but also on the computation abilities

numeric software tool

valuation:

• calculation effort

• result

• …

approach parameter:

• solver

• convergence criteria

• …

model properties:

• matrix structur

• matrix size

• symmetry

• …

case base

Eigen-

schaften

Einstell-

parameter

Bewertung

Eigen-

schaften

Einstell-

parameter

Bewertung

properties

parameter

valuation

system matrix:

[A]{x}={b}

multiphysics problem

simulation solution

Intelligent and Distributed Solving of Multiphysics Problems Coordinated by Software Agents - An Intelligent Approach for Decentralized

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205

of the resource, this is also considered and saved

together with the cases and their evaluations.

4.1.3 Result Evaluation

The evaluation of a case must be done after the

simulation is finished. Even bad tries must be saved,

so the configurations won’t be used again on a similar

problem. The most important evaluation criterion is if

the simulation was solved or not. Other criteria like

the computation time must be compared relative to

the computation abilities, like the random access

memory of the resource. The best evaluation can be

obtained by comparing different solver

configurations and their results.

4.2 Similarity to Other Cases

Often examples on case-based reasoning are using

only one attribute to compare cases. For the solver

configuration in simulations, cases are more complex

and can’t be described or compared by one parameter.

As described in chapter 4.1.1 the properties

additionally contain different kind of parameters.

There are parameters that have to match exactly and

parameters that should be in the same range to use the

same solver configuration. To measure the similarity

between a new case and the cases saved in the

database, the algorithm must take this into account. A

common function to name the similarity  between

two cases c1 and c2 with n different parameter and

with the weights w

is given by









 







 























 









is the similarity between the cases in one

parameter. So multi-conditional cases are compared

considering different kind of parameters. To create

such an algorithm with appropriate weights a set of

data is analyzed by an expert.

Due to the decentralized architecture of the MAS,

the data is distributed and must be collected as well

as exchanged. This is done by our incooperation

concept.

4.3 Incooperation Concept

The cases and the database must be integrated to the

existing MAS. Thus, the database is cared for by a

new agent, the case base agent. It manages the old

cases and is able to present similar cases for received

properties. Thus a message with the properties as

content is send. To save new cases into the database,

it can receive the cases by a new ACL message with

the id new_case. Figure 5 shows the new structure of

the MAS and the additionally needed communication

ways.

Figure 5: MAS with integrated case-based reasoning

approach.

The first step when using case-based reasoning for

a new model is to find the model properties that are

needed for the similarity measurement. Here, the

coordination agent that receives the model from a

user is responsible. It analyzes the model and sends

the properties to the case base agent. If there are

similar cases, it uses them for creating a prioritized

price list as a basis for the bidding process. If there

are no similar cases the previous concept is used for

creating the price list. If there are just one or two cases

yet, another configuration can be tried in the case that

there are more calculation resources left.

The calculation agents bid on the parts. Thus they

check if they match the computation abilities for the

parts and configurations in the price list. With this

method the agents can decide on their own whether

the case can be adapted for their current simulation

tasks or not. After each simulation, the calculation

agents evaluate the results by comparing their

solutions and send the cases to the case base agent.

With the presented incooperation concept, the

data for each physical domain is collected and saved

centrally but the agents keep their autonomy. The

case-based reasoning assists them by the choice on

which partial problem to bid.

5 CONCLUSIONS

In this paper a multi-agent system is presented, which

is able to solve different multiphysics simulations on

distributed computation resources. The basic

functionality is shown on a microwave oven example,

considering electromagnetic waves and the heat

transfer. The MAS has also been successfully tested

for further models. Because of the difficulties to

choose the right solver configuration, a concept to

case base

Eigen-

schaften

Einstell-

parameter

Bewertung

Eigen-

schaften

Einstell-

parameter

Bewertung

properties

parameter

valuation

case base

agent

coordination

agent

calculation

agent

manage

database

add new

cases

ask for / receive

similar cases

consider old

cases when

creating the

price list

evaluate

simulation

process

multi-agent communication

extended tasks

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

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incorporate a case-based reasoning approach is given.

The case-based reasoning is used to support the

decisions made by the agents in concern of the solver

configuration. This extension allows the MAS to

learn like a human expert from model to model. The

selection of an appropriate linear solver is only one

approach where the proposed MAS collects

knowledge. Further this approach can be extended to

the more complicated case of nonlinear and/or time

dependent problems. The MAS can be regarded as

intelligent assistant system for multiphysics

simulations. It enables inexperienced users to

simulate complex problems on distributed, already

available resources using proven software tools.

ACKNOWLEDGEMENTS

The authors would like to thank the Deutsche

Forschungsgemeinschaft (DFG) for supporting the

project GekoProAg (RU 720/11-2 & WE 5312/8-2).

REFERENCES

Bellifemine, F., Caire, G., Greenwood, D., 2007.

Developing multi-agent systems with JADE. Wiley.

Beyer, T., Yousefifar, R., Göhner, P., Wehking, K.-H.,

2016. Agent-Based Dimensioning to Support the

Planning of Intra-Logistics Systems. IEEE 21st

International Conference on Emerging Technologies

and Factory Automation (ETFA).

Blasco, R., Marco, Á., Casas, R., Cirujano, D., Picking, R.,

2014. A smart kitchen for ambient assisted living.

Sensors, 14, pp. 1629-1653.

Boschert, S., Rosen, R., 2016. Digital twin—the simulation

aspect. In Mechatronic Futures, pp. 59-74, Springer

International Publishing.

Buchau, A., Rucker, W. M., Rain, O., Rischmüller, V.,

Kurz, S., Rjasanow, S., 2003. Comparison between

different approaches for fast and efficient 3-D BEM

computations. In: IEEE Transactions on Magnetics,

vol. 39, no. 3, pp. 1107-1110.

Clement, S. J., McKee, D. W., Romano, R., Xu, J., Lopez,

J. M., Battersby, D., 2017. The Internet of Simulation:

Enabling agile model based systems engineering for

cyber-physical systems. In: System of Systems

Engineering Conference (SoSE), pp. 1-6.

de Mantaras, R. L., 2001. Case-based reasoning. In:

Machine Learning and Its Applications, pp. 127-145,

Springer Berlin Heidelberg.

Dickinson, E. J., Ekström, H., & Fontes, E., 2014.

COMSOL Multiphysics®: Finite element software for

electrochemical analysis. A mini-review.

Electrochemistry communications, 40, pp. 71-74.

Fetzer, J., Kurz, S., Lehner, G., Rucker, W. M., Henninger,

P., Röckelein, R., 1999. Analysis of an actuator with

eddy currents and iron saturation: Comparison

between a FEM and BEM-FEM coupling Approach. In:

IEEE Transactions on Magnetics, vol. 35, no. 3, pp.

1793-1796.

Fipa, A. C. L., 2002. Fipa acl message structure

specification. Foundation for Intelligent Physical

Agents,

http://www.fipa.org/specs/fipa00061/SC00061G.html

(18.8. 2017).

Grabmaier, S., Jüttner, M., Vögeli, D., Rucker, W. M.,

Göhner, P., 2016. Numerical framework for the

simulation of dielectric heating using finite and

boundary element method. In: International Journal of

Numerical Modelling: Electronic Networks, Devices

and Fields.

Gupta, O. P., 2002. Finite and Boundary Element Methods

in Engineering. Balkema Publishers.

Jazdi, N., 2014. Cyber physical systems in the context of

Industry 4.0. In: IEEE International Conference on

Automation, Quality and Testing, Robotics, pp. 1-4.

Jennings, N., Wooldridge, M., 1996. Software agents. In

IEE review, 42(1), pp. 17-20.

Jüttner, M., Grabmaier, S., Vögeli, D., Rucker, W. M.,

Göhner, P., 2017. Coupled Multiphysics Problems as

Market Place for Competing Autonomous Software

Agents, In: IEEE Transactions on Magnetics, Vol. 53,

Issue 6.

Lambersky, V., 2012. Model based design and automated

code generation from Simulink targeted for TMS570

MCU. In: Education and Research Conference

(EDERC), pp. 225-228.

Meister, A., 2015. Numerik linearer Gleichungssysteme.

Springer Spektrum, Vol 5.

Mozumdar, M. M. R., Gregoretti, F., Lavagno, L.,

Vanzago, L., Olivieri, S., 2008. A framework for

modeling, simulation and automatic code generation of

sensor network application. In: 5th Annual IEEE

Communications Society Conference on Sensor, Mesh

and Ad Hoc Communications and Networks, 2008.

SECON'08, pp. 515-522.

Tolk, A., 2016. Tutorial on the engineering principles of

combat modeling and distributed simulation. In:

Proceedings of the 2016 Winter Simulation

Conference, pp. 255-269.

Vázquez, M., Houzeaux, G., Koric, S., Artigues, A.,

Aguado-Sierra, J., Arís, R., Taha, A., 2016. Alya:

Multiphysics engineering simulation toward exascale.

In: Journal of Computational Science, 14, pp. 15-27.

Zhang, X., Gao, H., Guo, M., Li, G., Liu, Y., Li, D., 2016.

A study on key technologies of unmanned driving.

CAAI Transactions on Intelligence Technology, 1, pp.

4-13.

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Simulations

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