Product Suggestions

Post your suggestions on new features and products.

MapleSim is a mature product. The rich component library leaves little room for improvement for wide range of applications. It is understandable that latest product releases focused on specialized toolboxes and performance improvements.

Here is what I think could be beneficial for many users, which is not related to performance, but can help improve the user experience:

  1. Crossing connection lines: A view option to render a crossing connection line with an arc at the crossing point of two connection lines of the same type. Right-click on a connection line might be enough.

    -> To avoid misinterpretations of routing in crowded model diagrams
  2. Parameters: An option to populate or reset changes in the parameter pane to the parameter default settings view and vice versa

    -> When testing or optimizing a model, sometimes changed parameters should become default values or be reset. Doing this manually is error prone and takes time.
  3. Component flip: Selecting more than one component including connection lines and applying a flip to all of them

    -> When building a model, it can happen that a nicely laid out arrangement of components needs to be mirrored or rotated in its entirety. Doing this component by component and connection by connection is a lot of work that can be saved by this option.
  4. Initial conditions: An option in the view menu to highlight components where ICs have been changed from ignore to treat as guess or to strictly enforce

    -> ICs are set for many purposes. In addition to defining ICs needed for simulations, this can include extracting equations, testing different model states, or temporarily "immobilizing" a model during assembly, to name a few. Undoing a tentative change can easily be forgotten. Combining existing models that work on their own into a new more complex model often results in an overly constrained model that either cannot be assembled or does not simulate.
    In debugging a model, ICs of all components must be individually inspected. This takes time. A quick overview that shows components where ICs are not set to ignore would be very helpful in debugging models.
  5. Undo Create subsystem: A reverse operation that inserts the contents of a subsystem into a parent subsystem.

    -> With the evolution of a model it is sometimes useful to exclude or include existing components from or to a subsystem. For this purpose, an undo create subsystem operation should preserve existing connections. A time saver.
  6. Subsystem ports: An option to align a subsystem port to the drawing grid to remove “micro” steps in connection lines

    -> For perfectionists who do not have the time to learn (and remember) how to fine-tune at the component level
  7. A history or log function of user actions changing a model, its parametrization or internal state.

    -> Often a model does not simulate at all or as desired after modifications. Restoring to a configuration that worked by undo only goes back to the last simulation performed. In such a situation, only reloading the latest file version and redoing modifications may restore the desired model, parametrization, or state. This takes time and migth be unsuccessful. A record of user actions would be a great help.
    History or log information in file format could also help MapleSim support to reproduce an error.

For me personally, reducing errors (4. > 7. > 2.) would improve the use experience much more than layouting aids (3. > 1., 5., 6.).

Hi, just some ideas for improvement!

- since MapleFlow uses Maple as its engine, more integration of MapleFlow and Maple would be nice. Some commands that work very well in Maple not always work the same in MapleFlow. For example, BodePlot plots magnitude and phase in Maple but plots only magnitude in MapleFlow

- a better Help documentation would also help. ?command/function works in Maple but not in MapleFlow. It's a bit anoying to have to open Maple just to get help documentation

- a lot of palettes are not enabled in MapleFlow. Again, it is a little anoying to have to open Maple to get some of the palettes copied and pasted into MapleFlow

Auto paste last entry

So maple uses % as the last expression entry.  My suggestion is to use Crtl+Space on the % command to re-display the last expression.  Yes one could easily use the mouse to select the last entry then Crtl+c and Crtl+v. 

Or maybe the command Crtl+Shift+L to auto paste last entry. 

**edit** actually I would prefer the Crtl+Shift+L option to auto paste the last entry.

** Appears to be a suggestion I made earlier

December and Maple 2021.2 have both arrived, which means that we can look forward to year 2022 and Maple 2022.

        What should we like to find new in Maple 2022?  Here follow a few suggestions, to which readers of Maple Primes can add.

        In my opinion the weakest feature of Maple 2021 is the solution of integral equations.  Even when this package was first introduced into Maple, a couple of decades ago, it was weak, applicable to only linear such equations.  A quarter century earlier, David Stoutemyer (a true genius and entrepreneur, originator of Mu-Math, Mu-Lisp, Derive and computer-algebra capabilities incorporated in calculators of Texas Instruments) had published code for non-linear integral equations, based on Reduce.  There is a Handbook of Integral Equations by Polyanin and Manzhirov that lists about 2000 solutions of integral equations.  Let Maple 2022 be the basis of a boast by Maplesoft for Maple to be able to solve 96 per cent of those equations, in the same way that Edgardo Cheb-Terrab can (rightfully) boast that Maple can solve 96 per cent of differential equations in a standard compilation.  Any differential equation can, apparently, be converted to an integral equation, whereas the converse is not true.  For this reason alone, the development of solution of integral equations should become a priority to assist users of Maple.

        Another area worthy of expansion and enhancement is the solution of differential equations in terms of Heun functions; that capability is already present, but working with those functions in their present form is difficult and slow.  The inclusion of related functions, such as Lame functions, into Maple is long overdue.  Although efforts have been devoted to the development of the physics package in recent years, culminating in a tremendous achievement of capability, only a few physicists in the world can appreciate that luxury, whereas the solution of differential, and integral, equations permeates all science and engineering. 

          What items are on your list of wishes for Maple 2022?

A simple suggestion...

I would appreciate being able to open multiple help pages simultaneously instead of just one.
This seems to me particularly interesting when you have to browse back and forth between several related items.

Guys, this is still the most painful thing i Maple for me, and I hope this gets a high priority for future development.

It is still not possible to compare variables, when one of them could become zero.


[`*`, `+`, `-`, `/`, `<`, `<=`, `<>`, `=`, Im, Re, `^`, abs, add, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, cos, cosh, cot, coth, csc, csch, csgn, diff, eval, evalc, evalr, exp, expand, factor, floor, frac, int, ln, log, log10, log2, max, min, mul, normal, polar, root, round, sec, sech, seq, shake, signum, simplify, sin, sinh, sqrt, surd, tan, tanh, trunc, type, verify]


a := 15*Unit('kN')



b := 0*Unit('kN')




if a < b then "True" else "False" end if

Error, cannot determine if this expression is true or false: 15*Units:-Unit(kN) < 0




Has this ever happened to you? You’re using Maple Learn, and having a grand old time, but suddenly! The horror! You notice a bug! Of course, it’s a shocking experience to realize that our products are not, in fact, flawless, but unfortunately it’s true. There are bugs. But, what’s this? There’s a glimmer of hope on the horizon… the Flag a Problem button! By using the Flag a Problem button, you can let us know about the problem you found, and with the power of our mighty development team, we’ll fix it! Yes, with our forces combined… we can defeat all of these bugs!

A picture of the Flag a Problem button with glowing rays surrounding it.

In all seriousness, we really do appreciate your feedback. Whether you’ve spotted a bug or are looking for a new feature, let us know! We’re constantly updating and improving Maple Learn, and user feedback is a hugely important part of this process. For example, we had a user suggest that Maple Learn treat Δt as a single entity, as in physics that notation is used to mean a change in time rather than Δ times t. And we’re happy to announce that this is now a feature! Here’s just a taste of some of the other things we’ve changed based on user feedback:

  • Can now use the Context Panel to evaluate operations with matrices
  • Maximum number of intersection points shown has increased to 20
  • Intersection points now shown for parametric equations and circles
  • Using the Context Panel no longer scrolls the page
  • Quick Actions menu no longer parameterizes the f of f(x)
  • Fixed display bug for inverse trig functions

Evidently, not every piece of feedback we get is a feature request. Sometimes there’s bugs! And we want to hear about those too. In all honesty, I think it’s pretty neat to see the bugs I’ve reported being fixed. It wasn’t too long ago that I noticed a small error with tables—when the header of the table had a subscript, pressing the down arrow jumped to the next group instead of the next row. I reported it, and now it’s fixed! I can’t help but feeling a little smug, like I’m the one who fixed it. Of course, the credit for the actual code goes to our developers. But it is also true that they wouldn’t have fixed it if no one had pointed it out. Truly, teamwork makes the dream work. And if you want to feel smug about the bug you pointed out being fixed, or the feature you asked for being added, then head on over to that Flag a Problem button. Let us know what you want to see and we’ll listen. What’s more, we’ll be making more posts every now and then to let you know about what’s new with Maple Learn and what we’ve changed based on your feedback. That way you have something to print out and frame on your wall as proof of the contribution you’ve made to Maple Learn! (Or I suppose you could just read it. But where’s the fun in that?)

In the context of analyzing physical systems I often have to plot results in the form of y=f(x,a,b,c,…). Here the plot variables x and y are physical quantities and the system parameters a,b,c… can have units as well.

After substitution of parameters the expression f(x,a,b,c,…) can be plotted using plot(f(x,a,b,c,…),x_range). Unit choice and labeling of the abscissa work already well when x_range is given in the format x=x0..x1 (where x0 and x1 have a value and a unit). This is already a huge improvement since labeling and unit conversion errors on the abscissa are almost impossible.

Also, the units on the ordinate are correctly displayed. However, if the depended variable y is desired to be displayed on the ordinate it must be added by hand using the label option. In doing so the display units and labels of both axes must be re-entered by hand. This re-entering step is a source of labeling and conversion errors.

To improve ordinate labeling and to reduce conversion errors I would love to see two improvements:

  • A plot option that would allow unit conversion of plot axes. I.e. telling Maple in which units a physical quantity has to be displayed and forcing a rescaling of the values of the physical quantities.
  • With less priority and additional to expressions, the plot command should also accept equations in the form of y=f(x) as input. This would lead to a very compact syntax that produces content rich and, more importantly, correct plots of physical quantities. Wrong labeling and conversion errors would be very unlikely.

Overall, I am very pleased by Maples unit functionality. I have been reluctant to switch from my old work style of using names as unit placeholder and self-made conversion sets. But now I feel that the likelihood of producing unit conversion errors with my old work style has become higher than using Maples units.

I can only encourage interested users to give units a try. Its good!  For me it has turned out to be time worth invested.

I also hope that Maplesoft continues their efforts of providing more unit functionalities. It’s a big task but calculations with physical quantities are also a big differentiator.  

... and two suggestions to the development team

In ?DiscreteValueMap (package Statistics) it's given an example concerning rhe Geometric distribution along with this comment:
"The Geometric distribution is discrete but it necessarily assumes integer values, so (bold font is mine) it also does not have a DiscreteValueMap"

This sentence seems to indicate that "because a distribution is discrete over the set of integers, it cannot have a DiscreteValueMap", some sort of logical implication...

But my feeling is that the Geometric distribution (or any other discrete distribution) does not have a DiscreteValueMap because this attribute has just not been specified when defining the distribution.


GeomRV := RandomVariable(Geometric(1/2)):
f := unapply(ProbabilityFunction(GeomRV, n), n):

AnotherGeomRV := Distribution(
DiscreteValueMap(AnotherGeomRV , n);

Thus having the set of natural numbers as support doesn't imply that DiscreteValueMap cannot exist.

Suggestion 1: modify the ?DiscreteValueMap help page so that it no longer suggests that some discrete distributions cannot have a .DiscreteValueMap 


I think there exists a true problem with the definition of discrete distributions in Maple: the ProbabilityFunction of a (discrete) random variable) takes non zero values outside their definition set.
For instance

ProbabilityFunction(GeomRV, Pi);  # something non null

To ivercome this problem I defined a new Geometric distribution this way (not entirely satisfying):


GeomRV := RandomVariable(Geometric(1/2)):
f := unapply(ProbabilityFunction(GeomRV, n), n):
g := n -> (1-ceil(n-floor(n)))*f(n)    # (1-ceil(n-floor(n))) = 1 if n in Z, 0 otherwise

AnotherGeomRV := Distribution(
      'DiscreteValueMap'=(n->n),  # is wanted
ProbabilityFunction(AnotherGeomRV, 2);
ProbabilityFunction(AnotherGeomRV, Pi);

PS: None of the statistics based upon the  ProbabilityFunction (Mean, Variance, ... ) is correctly computed with the previous construction. This could be easily overcome by completing this definition, just as its done in Maple, for all the requires statistics, for instance 

AnotherGeomRV := Distribution(
      'Mean'=1   # or more generally (1-p)/p form Geometric(p)

Suggestion 2: modify the way discrete distributions are defined in Maple in order to avoid ProbabilityFunction to return wrong values.

Equation labels are great!

I use them extensively to produce textbook style documentation that is understandable for non-Maple users. Even if Maple input is not hidden, documents look much cleaner since auxiliary names and the assignment statement “:=” do not have to be used most of the time.

Suggestions to improve Maple 2021 equation label functionality (in order of preference):

  • In a text passage or Maple input: Double click on a label reference to open the insert label dialogue (crtl-L) in order to change the reference (instead of deleting the reference and inserting a new reference).
  • Right click on an equation label to hide it with the context menu. Or right click on the output and have a “show/hide label" option.
  • After a document is finished, input is hidden and before printout/export is produced: A function that hides/shows all labels that are not referenced in text passages.
  • A search function for equation labels in a document, or alternatively: a pallet simliar to the variable pallet to manage labels.
  • Labels inside a text passage that refer to executable math with toggled input. This would allow the definition of expressions inside a text passage and use them in subsequent calculations. Example for a text passage: “If we insert for the mass m=15 kg in equation (33), the frequency response looks as follows:" plot(subs(label_of(whatever has been attributed to m=15kg),(33)),plot_range). This would reduce redundant entries in the document and potential mismatch between text and calculation results.
  • Renaming of single labels (i.e. assigning an alias) either by right click on the label or by a pallet.
  • Labels for non-executable math inside a text passage for further use in other text passages or later insertion in executable math.


  • There is another (not documented?) feature that is very handy: Double click on an equation label inserts the equation label at the cursor position. A nice time saver.
  • Only recently I found out that single equation labels can be hidden/removed using Format>Equation Labels>Selection. Since this option was always grayed out, I could not make sense out of it, because the text was not self-explanatory to me.  Instead of Format>Equation Labels>Selection a more self-explaining menu entry would be desirable. “show/hide selection” would already better describe the action behind the menu item. However, it is still not intuitive to select output in order to make equation labels disappear (that are by the way not highlighted in blue by the selection process when only a single output/execution group is selected). There are many reasons that could make a change to self-explaning menu items not that straight forward as it sounds. In this case a mouse-over is always helpful to get more explanations on a button or a menu item. Alternatively and probably better: It would be more straight forward to select or click onto labels to manipulate them. This of course only works for one label at the time, which in my case is the most common use case.
  • Equation labels are unique. They enable a work and documenting style that other math tools do not provide. If used consistently, they provide a new level of abstraction where explanatory text and computation can be combined in way that a mathematical interpreter (human or a smart machine) could proof results using only textbook style documents as input (e.g. pdf scans). At least, this is theoretically possible. However, I have noticed that many examples from users do not make use of equation labels. They are still pretty much done in a traditional programming style where loads of unnecessary variables are used. This is understandable since many people start mathematical problem solving with the aid of computers by programming. So new users to Maple use Maple pretty much the same way they were trained.
  • I am fully aware that there are many applications where equation labels are not the most efficient way of producing a result. But producing a result is different from documenting results or even documenting a mathematical proof.


The site contains free books in English and Russian along with software created under the guidance of the main author prof. V. Aladjev in such areas as general theory of statistics, theory of cellular automata, programming in Maple and Mathematica systems. Each book is archived, including its cover and book block in pdf format. The software with freeware license is designed for Maple and Mathematica.

Hello everyone,

There is a strange behaviour with code-edit. Namely, when hiding code-edit window and recovering it, sometimes Maple create a very narrow window. It is very hard to see the code that way. After a while the code-edit region window readjusts itself though. However it takes time.

Also another thing, it would be useful when searching in a worksheet, to have an option that allows to search in code-edit region also.

Best regards,

When this question was asked here earlier, I neglected to suggest or to emphasize two further items.  Now, on revising Mathematics for Chemistry with [Maple], I recognise that I should have included these two objectives for inclusion in Maple 2021.

- an extended and improved spreadsheet with symbolic capability; I suspect that Maple was the only software for symbolic computation to include such a facility, which sadly has become deprecated, for no obvious reason.

- a much extended capability to solve integral equations; publications dating from 1976 -- i.e. before Maple! -- have shown what is possible; Maple's capabilities for differential equations might still be superior, although the competition is becoming close, so further efforts in the development of both differential and integral equations are timely and appropriate.  Related to differential equations is naturally the extension of capabilities of special functions, both to extend present functions and to produce new functions, such as those of Lame.

We recently published a paper on multiscale-multidomain simulation of battery models.

Some challenges are listed at

Maple and symbolic math can play a critical role in solving many challenging problems. For example, consider a seemingly-trivial problem

uxx+uyy = 0

x = 0 and x = 1, ux = 0 for all y

y = 1, u = 0, for all x

y = 0, u =1, 0<=x<=0.5

y = 0, uy = 0, 0.5<x<=1

There is a singularity at (0.5,0) and most numerical methods will have trouble there. In these equations, uxx means the second derivative of u with respect to x.

Maple can help solve this problem with conformal mapping to achieve arbitrary precision. As of today, machine precision is not possible with any numerical method even with millions of Degrees of Freedom. The Maple code is given below. A FEM code is given below as well. Models like this can benefit from Maple adding parallel sparse direct and iterative solvers.





Digits := 15


 The domain is tranformed from Z = X+IY to w. The points tranformed are


Zdomain := [[0, 0], [1, 0], [1, 1], [0, 1]]



wdomain := [0, 1, 1+a, a+2]



eq1 := diff(Z(w), w) = -I*K1/(w^(1/2)*(w-1)^(1/2)*(w-a-1)^(1/2)*(w-a-2)^(1/2))


 a is not known apriori. The value of a should be found to make sure [1,1] in the Z coordinate is transformed to [1+a] in the w coordinate.


a := 2^(1/2)-1


 Value of K1 is found using the transformation of [1,0] to 1 in the w coordinate


eq11 := 1 = -K1*2^(1/2)*EllipticK(2^(1/2)/2)



K1 := -(1/2)*(2^(1/2)/EllipticK(2^(1/2)/2))


 The height Y in the Z coordinate is found by integrating from 1 to 1+a in the w coordinate.







 The choice of a = sqrt(2)-1 gives the height of 1 for Z coordinate.







 integration from 0 to 1+a in the w coordinate gives 1,1 in the Z coordinate.


EllipticF(2^(1/2)/(2+2^(1/2))^(1/2), 2^(1/2)/2)/EllipticK(2^(1/2)/2)





 Integrating w from 0 to wmid =1/sqrt(2) gives the point 0.5,0 in the Z coordinate


wmid := 2^(1/2)/2


 Next w domain is transformed to Z2 domain Z2 = X2+IY2


Z2domain := [[0, 0], [1, 0], [1, H], [0, H]]



wdomain2 := [0, 2^(1/2)/2, 2^(1/2), 2^(1/2)+1]



eq2 := diff(Z2(w), w) = -(2*I)*K2/(w^(1/2)*(4*w-2*2^(1/2))^(1/2)*(w-2^(1/2))^(1/2)*(w-2^(1/2)-1)^(1/2))


 K2 is found based on the transformation of wmid to [1,0] in Z2 coordinate.


eq21 := 1 = -2*K2*EllipticK(1/(((2+2^(1/2))^(1/2))))/(2^(1/2)+1)^(1/2)



K2 := -(1/2)*((2^(1/2)+1)^(1/2)/EllipticK(1/(((2+2^(1/2))^(1/2)))))


 The corner 0,1 in the Z coordinate is mapped by integrating eq2 from 0 to 1 in the w coordinate




1+EllipticF((2-2^(1/2))^(1/2), ((2^(1/2)+1)/(2+2^(1/2)))^(1/2))*I/EllipticK(1/(((2+2^(1/2))^(1/2))))



corner := 1.+.559419351518322*I


 This is the point 1,0 in the original coordinate.

 The height in the Z2 coorinate is found by integrating eq2 from wmid to 1+a.


ytot := EllipticK(((2^(1/2)+1)/(2+2^(1/2)))^(1/2))*I/EllipticK(1/(((2+2^(1/2))^(1/2))))





 The magnitude in the Y direction is given by the coefficient of I, the imaginary number


Ytot := EllipticK(((2^(1/2)+1)/(2+2^(1/2)))^(1/2))/EllipticK(1/(((2+2^(1/2))^(1/2))))


 The analytial solution in the Z2 corordinate is a line in Y2 to satisfy simple zero flux conditions at X2 = 0 and X2 = 1.


phianal := 1+b*Y2


 The value of phi is zero at Y2 = Ytot (originally the cathode domain in the Z domain)


bc := 1+b*EllipticK(((2^(1/2)+1)/(2+2^(1/2)))^(1/2))/EllipticK(1/(((2+2^(1/2))^(1/2)))) = 0



b := -EllipticK(1/(((2+2^(1/2))^(1/2))))/EllipticK(((2^(1/2)+1)/(2+2^(1/2)))^(1/2))


 The analytical solution is given by







 The potential at the corner is given by substituting the imaginary value of corner for Y2 in phinanal)


phicorner := 1-.559419351518322*EllipticK(1/(((2+2^(1/2))^(1/2))))/EllipticK(((2^(1/2)+1)/(2+2^(1/2)))^(1/2))





local flux/current density calculation, written in terms of w is


curr := -(2^(1/2)+1)^(1/2)*2^(1/2)*EllipticK(2^(1/2)/2)*(w-1)^(1/2)/(EllipticK(((2^(1/2)+1)/(2+2^(1/2)))^(1/2))*(4*w-2*2^(1/2))^(1/2))


average flux/current density calculation for the anode


currave := -(1/2)*((2^(1/2)+1)^(1/2)*(2^(1/2)-1)*EllipticK(2^(1/2)/2)*(2^(3/4)+2^(1/4)+arctanh(2^(3/4)/2))*2^(1/2)/EllipticK(2^(3/4)/2))



 The average current density at Y =0, local current density at X = 0,Y=0 and potential at X=1,Y=0 (Corner) can be used to study convergence of FEM and other numerical methods


-1.656507648777793388522396, -1.161311530233258689567781, .5414751796044734741869534




Download Conformalmapping.mws


This FEM code is for solving Laplace's equation with primary current distribution considered in Model 1.
This code is based on FEM weak-form. Biquadratic Lagrange shape functions (9nodes in an element) are used.



Lx:=1: #length in X

Ly:=1: #length in Y

nx:=10: #number of elements in X (even numbers only)

ny:=10: #number of elements in Y, to be kept same as nx in this version

hx:=Lx/nx: #element size x

hy:=Ly/ny: #element size y

Procedure to perform numerical integration on shape functions to obtain local matrices (can be replaced with analytical integration for this particular problem)
  -Shape functions are also used as weight functions in applying weak formulation. Numerical integration is done using Simpson's rule.
  -Local cartesian coordinates x,y are converted to natural coordinates zeta and eta. This transformation is not required for this simple geomerty but useful in general. zeta and eta are obtained by scaling x and y with hx/2 and hy/2, respectively, in this code.


global Kx,Ky,Nx,Ny,zeta,eta,c;
local A,dAdzeta,dAdeta,y,x,J,terms,i,j,k,l,dx,dy,fx,fy,fxy,fyy,dzeta,deta,J1,J2;

A:=[(1-zeta)*zeta*(1-eta)*eta/4,-(1-(zeta)^2)*(1-eta)*eta/2,-(1+zeta)*zeta*(1-eta)*eta/4,(1-(eta)^2)*(1+zeta)*zeta/2,(1+zeta)*zeta*(1+eta)*eta/4,(1-(zeta)^2)*(1+eta)*eta/2,-(1-zeta)*zeta*(1+eta)*eta/4,-(1-(eta)^2)*(1-zeta)*(zeta)/2,(1-(zeta)^2)*(1-(eta)^2)]; #bi quadratic langrange shape functions









terms:=20:#number of terms for numerical integration

for i from 1 to nops(Nx) do #loop to obtain local matrices      

for j from 1 to nops(Ny) do

for k from 0 to terms do #outer loop double integration, integration in zeta

if k = 0 then fx[k]:= subs(zeta=-1,Nx[i]*Nx[j]*J); fy[k]:= subs(zeta=-1,Ny[i]*Ny[j]*J);  
elif k = terms then
fx[k]:= subs(zeta=-1+(k*dzeta),Nx[i]*Nx[j]*J);
fy[k]:= subs(zeta=-1+(k*dzeta),Ny[i]*Ny[j]*J);  
elif irem(k,2) = 0 then
fx[k]:= 2*subs(zeta=-1+(k*dzeta),Nx[i]*Nx[j]*J);
fy[k]:=     2*subs(zeta=-1+(k*dzeta),Ny[i]*Ny[j]*J);
else fx[k]:= 4*subs(zeta=-1+(k*dzeta),Nx[i]*Nx[j]*J);
fy[k]:=     4*subs(zeta=-1+(k*dzeta),Ny[i]*Ny[j]*J);  end if;

for l from 0 to terms do #inner loop double integration, integration in eta

if l = 0 then fxy[l]:= subs(eta=-1,fx[k]); fyy[l]:= subs(eta=-1,fy[k]);
elif l = terms then fxy[l]:= subs(eta=-1+(l*deta),fx[k]); fyy[l]:= subs(eta=-1+(l*deta),fy[k]);
elif irem(l,2) = 0 then fxy[l]:= 2*subs(eta=-1+(l*deta),fx[k]); fyy[l]:= 2*subs(eta=-1+(l*deta),fy[k]);
else fxy[l]:=4*subs(eta=-1+(l*deta),fx[k]); fyy[l]:=4*subs(eta=-1+(l*deta),fy[k]); end if;

end do;
end do;
end do;
end do:

end proc:

n:=nx*ny; #total number of elements

n := 100


Nx1:=nx*2+1: #number of nodes in x in one row

N:=Nx1*(2*ny+1); # total number of nodes/equations

N := 441


K:=Matrix(N,N,storage=sparse): # global K matrix

C:=Vector(N,storage=sparse): # global c matrix

L2G:=Matrix(n,9):  #mapping matrix - each row has node numbers for each element

localmatrices(hy/2,hy/2,hy/2,hx/2,hx/2,hx/2,0,0): kx:=copy(Kx):ky:=copy(Ky):c0:=copy(c):

for i from 1 to n do #modifying,adding and assembling matrices to get global matrix
if i<=nx/2 then  
a1:=copy(kx); a2:=copy(ky); a3:=0; a1[1..3,1..9]:=IdentityMatrix(3,9); a2[1..3,1..9]:=Matrix(3,9,shape=zero); a4:=a1+a2; c:=copy(c0); c[1..3]:=1.0;

elif i=nx/2+1 then  a1:=copy(kx); a2:=copy(ky); a3:=0; a1[1,1..9]:=IdentityMatrix(1,9); a2[1,1..9]:=Matrix(1,9,shape=zero); a4:=a1+a2; c:=copy(c0); c[1]:=1.0;

elif i>nx*(ny-1) then a1:=copy(kx); a2:=copy(ky); a3:=0; a1[5..7,5..7]:=IdentityMatrix(3,3);
a1[5..7,8..9]:=ZeroMatrix(3,2); a2[5..7,1..9]:=Matrix(3,9,shape=zero); a4:=a1+a2; c:=copy(c0); c[5..7]:=0;

else a1:=kx; a2:=ky; a3:=0;a4:=a1+a2; c:=c0;  end if;


if k>nx then k:=1; l:=l+Nx1+3;

else l:=l+2; end if:



for i1 from 1 to 9 do
end do:

end do:

phi:=LinearSolve(K,C,method=SparseLU): #linear set of equations solved using Sparse LU solver


phi_at(1, 0) := .546587799122513





current_at(0, 0) := -1.15773815354626


if irem(nx/2,2)=0
then current_at(0,0.25):=add(dNdy_bottom_left[i]*phi[L2G[nx/4+1,i]],i=1..nops(Ny));
end if;

dNdy_bottom_center := [0, -30, 0, 0, 0, -10, 0, 0, 40]

current_at(0, .25) := -1.26989097821724





Download FEM_2D.mws

What are the things you most like to see improved/add to next version of Maple? 

This is my list for a starter:

1.  Improve the debugger. Debugger is very useful but needs more work. At least be able to see code listing in larger view as one steps in for example. See Matlab debugger for inspiration.

2.  Improve Latex. It still does not do fractions well. Posted about this before.

3. Eliminate hangs when using timelimit(). On long runs, random hangs happen when timelimit() do not expire as requested. Posted about this before.



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