By K. Merten (auth.), R. E. Bank, K. Merten, R. Bulirsch (eds.)
Numerical simulation and modelling of electrical circuits and semiconductor units are of primal curiosity in modern day excessive expertise industries. on the Oberwolfach convention greater than 40 scientists from all over the world, in cluding utilized mathematicians and electric engineers from and universities, awarded new leads to this zone of starting to be significance. The contributions to this convention are awarded in those court cases. They comprise contributions on targeted themes of present curiosity in circuit and machine simulation, in addition to contributions that current an outline of the sphere. within the semiconductor sector distinct lectures got on combined finite aspect tools and iterative tactics for the answer of huge linear platforms. for 3 dimensional types new discretization systems together with software program applications have been offered. Con nections among semiconductor equations and the Boltzmann equation have been proven in addition to family members to the quantum delivery equation. different concerns mentioned during this region contain the layout of simulation courses for semiconductors, vectorcomputers, and interface difficulties in different dimensions. themes mentioned within the sector of circuit simulation comprise the index class of differential-algebraic platforms, connections with ill-posed difficulties, and regularization options. break up discretization strategies got for the effective calculation of periodic options of circuits taking into acount the latency. Homotopy equipment and new numerical suggestions for differential-algebraic platforms have been awarded, and im provements of targeted numerical equipment for traditional software program programs have been sug gested. The editors VII desk of Contents Circuit Simulation Merten K.
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Additional resources for Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices: Proceedings of a Conference held at the Mathematisches Forschungsinstitut, Oberwolfach, October 30 – November 5, 1988
Example text
Resistcnce branches controlled by currents. nches are ordered correspondin[)ly and partition the vectors e and i of voltages and currents in the same way. Then the device equations for the four kinds of branches are: 1. i 1 =C(e 1 )ei ' 2. i 2 =o(e 2 )-qr(t) with 9(0)=0 , 3. e 3 =L(i 3 )i 3 ' 4. e 4 =r(i 4 )-qE(t) with r(o)=o • No~ qI(t) ~nd qE(t) represent the external current and voltaGe sources; t:,e controlled sources are included in the nonlinear vector 22 functions g(e 2 ) and r(i 4 ). C(e 1 ) and L(i 3 ) are sparse symmetric and positive definite matrices, and their off-diagonal entries are constant.
Let the struCture of the circuit be described by the incidence matrix A, the rows and columns of which correspond to the nodes and branches respectivelye We distinguish between four kinds of branches: 1. ca~acity branches controlled by voltages, 2. 1) 3. induct8nce brunches controlled by currents, 4. resistcnce branches controlled by currents. nches are ordered correspondin[)ly and partition the vectors e and i of voltages and currents in the same way. Then the device equations for the four kinds of branches are: 1.
4). 9) is an explicit ODE. The existence of the mentioned difficulties indicates a higher index situation, at least locally. 4) is solved by XEO in the case QI(t)50, QE(t)ao. 3) corresponding to the * 0, -qE'* • constant source vector q>I wit h t h e components A2 qI' + *. We have to take only q =0 and q =q , again the index-i-property guarantees the feasibility of the proposed embedding method via source amplification. 9) have to be reduced further. e. their sufficiently exact simulation leads to an index-i-problem.
